Unit 5 Geometry Test

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Unit 5 Geometry Test - Quiz

Questions and Answers
  • 1. 

    The dining room in Monticello, Thomas Jefferson's home in Virgina, is 216 inches by 222 inches. Of the following, which size rug would be similar in shape to the dining room rug?

    • A.

      72 in by 74 in

    • B.

      108 in by 110 in

    • C.

      118 in by 111 in

    • D.

      84 in by 96 in

    Correct Answer
    A. 72 in by 74 in
    Explanation
    The size of the dining room rug is 216 inches by 222 inches. To find a rug that is similar in shape, we need to find a rug with a similar ratio of length to width. The ratio of length to width for the dining room rug is 216/222, which simplifies to 0.973. Among the given options, the rug with the closest ratio is 72 in by 74 in, which has a ratio of 0.973. Therefore, the 72 in by 74 in rug would be similar in shape to the dining room rug.

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  • 2. 

    A 9-foot street sign casts a 12-foot shadow. The lamp post next to it casts a 24-foot shadow. How tall is the lamp post?

    • A.

      24 feet

    • B.

      15 feet

    • C.

      18 feet

    • D.

      36 feet

    Correct Answer
    C. 18 feet
    Explanation
    The height of the lamp post can be determined by setting up a proportion between the height of the street sign and its shadow, and the height of the lamp post and its shadow. Since the street sign is 9 feet tall and casts a 12-foot shadow, the ratio of height to shadow is 9:12. Using this ratio, we can find the height of the lamp post by setting up the proportion 9/12 = x/24, where x represents the height of the lamp post. Solving for x, we find that x = 18 feet. Therefore, the height of the lamp post is 18 feet.

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  • 3. 

    An isosceles triangle has two sides that are equal in length. Isosceles triangle ABC is similar to triangle XYZ. Determine which proportion you would use to find the length of the third side of triangle XYZ.

    Correct Answer
    C.
    Explanation
    To find the length of the third side of triangle XYZ, we can use the proportion of the corresponding sides of the two similar triangles. Since triangle ABC is similar to triangle XYZ, the corresponding sides are in proportion. Therefore, we can use the proportion of the lengths of the sides of the two triangles to find the length of the third side of triangle XYZ.

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  • 4. 

    You decide to use a scale of 1 inch: 8 feet to make a scale drawing of your classroom. If the actual length of your classroom is 36 feet, what should the length of your classroom be in the scale drawing?

    • A.

      1 inch

    • B.

      4.5 inches

    • C.

      36 inches

    • D.

      288 inches

    Correct Answer
    B. 4.5 inches
    Explanation
    The scale of 1 inch: 8 feet means that 1 inch on the scale drawing represents 8 feet in real life. If the actual length of the classroom is 36 feet, we can calculate the length in the scale drawing by dividing 36 by 8. This gives us 4.5 inches, which is the length of the classroom in the scale drawing.

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  • 5. 

    Lucy drew this scale drawing to show the triangular flower bed that she wants to build in her yard. Based on the drawing, what will be the area of the actual flower bed?

    • A.

      A=96 square feet

    • B.

      A=192 square feet

    • C.

      A=3 square feet

    • D.

      A=1.5 square feet

    Correct Answer
    A. A=96 square feet
    Explanation
    Based on the given scale drawing, the area of the actual flower bed will be 96 square feet.

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  • 6. 

    The two rectangles represent windows that are similar. Use the measurements to determine the height of the bigger window.

    • A.

      2.6 feet

    • B.

      15.6 feet

    • C.

      4.6 feet

    • D.

      3.9 feet

    Correct Answer
    D. 3.9 feet
    Explanation
    The height of the bigger window can be determined by comparing the measurements of the two rectangles. Since the rectangles represent similar windows, their corresponding sides are proportional. By using the given measurements, we can set up a proportion to find the height of the bigger window. Since 2.6 feet corresponds to 15.6 feet in the smaller window, and we are trying to find the height of the bigger window, we can set up the proportion 2.6/15.6 = x/4.6. Solving for x, we find that x is equal to 3.9 feet.

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  • 7. 

    Find the values of x in the triangle.

    • A.

      X=8 degrees

    • B.

      X=13 degrees

    • C.

      X=16 degrees

    • D.

      X=29 degrees

    Correct Answer
    D. X=29 degrees
    Explanation
    The values of x in the triangle are 8 degrees, 13 degrees, 16 degrees, and 29 degrees.

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  • 8. 

    Which of these side lengths could be used to make a triangle?

    • A.

      6 cm, 6 cm, and 4 cm

    • B.

      12 ft, 10 ft, and 29 ft

    • C.

      5 in, 7 in, 12 in

    • D.

      20 in, 20 in, 50 in

    Correct Answer
    A. 6 cm, 6 cm, and 4 cm
    Explanation
    The side lengths 6 cm, 6 cm, and 4 cm could be used to make a triangle. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, 6 cm + 6 cm = 12 cm, which is greater than 4 cm. Similarly, 6 cm + 4 cm = 10 cm, which is greater than 6 cm. Therefore, these side lengths satisfy the triangle inequality theorem and can form a triangle.

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  • 9. 

    Chantel constructs a triangle with angle measures 65 degrees and 38 degrees. What must be true of the measure of the third angle in her construction?

    • A.

      It must measure exactly 77 degrees.

    • B.

      It must measure exactly 87 degrees.

    • C.

      It can have any measure less than 103 degrees.

    • D.

      It can have any measure greater than 27 degrees.

    Correct Answer
    A. It must measure exactly 77 degrees.
    Explanation
    The sum of the angles in a triangle is always 180 degrees. Therefore, if Chantel constructs a triangle with angle measures of 65 degrees and 38 degrees, the measure of the third angle can be found by subtracting the sum of the other two angles from 180 degrees. 180 - (65 + 38) = 77 degrees.

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  • 10. 

    Josh constructs a triangle with angles measuring 54 degrees, 23 degrees, and 103 degrees. He wants to construct a different triangle with those angle measurements. What will he find if he does?

    • A.

      It is not possible to construct a different triangle with those angles measures.

    • B.

      Any other triangle he constructs with those angle measures will be congruent to his original triangle.

    • C.

      Any other triangle he constructs with those angle measures will be similar to his original triangle.

    • D.

      He can construct many other triangles with those angle measures, and none of them will be similar to the first triangle he constructed.

    Correct Answer
    C. Any other triangle he constructs with those angle measures will be similar to his original triangle.
    Explanation
    If Josh constructs a different triangle with angles measuring 54 degrees, 23 degrees, and 103 degrees, he will find that any other triangle he constructs with those angle measures will be similar to his original triangle. This is because triangles with the same angle measures are always similar, meaning they have the same shape but possibly different sizes. Therefore, no matter how Josh constructs a triangle with those angle measures, it will always have the same shape as his original triangle.

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  • 11. 

    Identify the cross section of this pyramid.

    • A.

      Triangle

    • B.

      Square

    • C.

      Point

    • D.

      Circle

    Correct Answer
    B. Square
    Explanation
    The cross section of a pyramid is the shape that is formed when the pyramid is cut by a plane parallel to its base. In this case, the cross section is a square because the pyramid is cut parallel to its base, resulting in a shape that has four equal sides and four right angles.

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  • 12. 

    When slicing a cone vertically through the vertex, what will be the shape of the resulting cross section?

    • A.

      Circle

    • B.

      Triangle

    • C.

      Ellipse (oval)

    • D.

      Square

    Correct Answer
    B. Triangle
    Explanation
    When a cone is sliced vertically through the vertex, the resulting cross section will be a triangle. This is because the intersection of the plane with the cone forms a triangle shape. The base of the triangle is the circular base of the cone, and the two sides of the triangle are formed by the slanted surface of the cone converging at the vertex. Therefore, the correct answer is triangle.

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  • 13. 

    Which is the shape of the cross section formed when the pyramid is sliced by the plane as shown? (The base is not a right triangle)

    Correct Answer
    A.
  • 14. 

    What is the shape of the cross section formed when the square pyramid is sliced by a plane perpendicular to its base that does not pass through its top vertex?

    • A.

      Parallelogram (not a square)

    • B.

      Square

    • C.

      Trapezoid

    • D.

      Triangle

    Correct Answer
    C. Trapezoid
    Explanation
    When a square pyramid is sliced by a plane perpendicular to its base, the resulting cross section will be a trapezoid. This is because the plane intersects the pyramid in a way that one side of the trapezoid is parallel to the base of the pyramid, while the other side is shorter and slanted. The shape does not form a square because the slanted side creates a shorter length.

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  • 15. 

    Find the circumference of the circle using the figure below. Use 3.14 for . Round to the nearest whole number. (C=)  

    • A.

      198 cm

    • B.

      150 cm

    • C.

      99 cm

    • D.

      63 cm

    Correct Answer
    A. 198 cm
    Explanation
    Based on the figure provided, it appears that the circle's diameter is 63 cm. The circumference of a circle can be calculated using the formula C = πd, where d is the diameter. Therefore, the circumference of this circle would be 3.14 * 63 = 198 cm.

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  • 16. 

    The coin pictures has a radius of 26.5 millimeters. What is the approximate area of one side of the coin?

    Correct Answer
    D.
    Explanation
    The approximate area of one side of the coin can be calculated using the formula for the area of a circle, which is A = πr^2. Given that the radius of the coin is 26.5 millimeters, we can substitute this value into the formula to find the area.

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  • 17. 

    A circle has an area of  and a radius of 4 in. What is the circumference of the circle?

    • A.

      50.24 in

    • B.

      25.12 in

    • C.

      46 in

    • D.

      12.56 in

    Correct Answer
    B. 25.12 in
    Explanation
    The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, the radius is given as 4 in. Plugging this value into the formula, we get C = 2π(4) = 8π. To find the numerical value, we can use an approximation of π as 3.14. Therefore, C ≈ 8(3.14) = 25.12 in.

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  • 18. 

    Jordyn has a circular flower bed with a diameter of 18 feet in her yard. Approximately how many square feet of her yard is covered by the flower bed? 

    • A.

      81 square feet

    • B.

      254 square feet

    • C.

      57 square feet

    • D.

      1017 square feet

    Correct Answer
    B. 254 square feet
    Explanation
    The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. In this case, the diameter is given, so we can divide it by 2 to find the radius. The radius is 18/2 = 9 feet. Plugging this value into the formula, we get A = π(9^2) = 81π square feet. Since we are asked for an approximate answer, we can use the approximation π ≈ 3.14. Multiplying 81 by 3.14, we get approximately 254 square feet.

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  • 19. 

    Find the value of x in the figure shown.

    • A.

      4 degrees

    • B.

      17 degrees

    • C.

      39. 5 degrees

    • D.

      70 degrees

    Correct Answer
    B. 17 degrees
    Explanation
    In the figure shown, x is the angle opposite to the angle labeled 17 degrees. According to the properties of a triangle, the sum of all angles in a triangle is 180 degrees. Since the angle labeled 17 degrees is opposite to x, we can conclude that x must also be 17 degrees.

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  • 20. 

    In the diagram shown, . What is the

    • A.

      18 degrees

    • B.

      108 degrees

    • C.

      36 degrees

    • D.

      144 degrees

    Correct Answer
    B. 108 degrees
  • 21. 

    Find the value of x in the figure.

    • A.

      85 degrees

    • B.

      17 degrees

    • C.

      19 degrees

    • D.

      5 degrees

    Correct Answer
    B. 17 degrees
  • 22. 

    Find the value of x in the figures shown.

    • A.

      34 degrees

    • B.

      66 degrees

    • C.

      151 degrees

    • D.

      156 degrees

    Correct Answer
    D. 156 degrees
    Explanation
    The value of x in the figures shown is 156 degrees.

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  • 23. 

    A right triangular prism and its dimensions are shown below. What is the total surface area, in square inches, of the right triangular prism?

    Correct Answer
    A.
    Explanation
    To find the total surface area of a right triangular prism, we need to calculate the area of each face and then add them up. The prism has two triangular faces and three rectangular faces. The area of each triangular face can be calculated using the formula 1/2 * base * height. The area of each rectangular face can be calculated by multiplying the length and width. Once we have calculated the area of each face, we can add them up to find the total surface area of the prism.

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  • 24. 

    Find the volume of the solid. Round your answer to the nearest hundredth if necessary. (Volume of a Circle = )

    • A.

      235.62 square centimeters

    • B.

      203.78 square centimeters

    • C.

      942.48 square centimeters

    • D.

      119.93 square centimeters

    Correct Answer
    A. 235.62 square centimeters
  • 25. 

    Find the surface area of the prism.

    • A.

      45 square feet

    • B.

      94 square feet

    • C.

      104 square feet

    • D.

      60 square feet

    Correct Answer
    B. 94 square feet
  • 26. 

    Find the area of the semicircle. Use 3.14 for . Round to the nearest tenth of necessary. (A=)

    • A.

      11.9 square yards

    • B.

      22.7 square yards

    • C.

      23.9 square yards

    • D.

      45.3 square yards

    Correct Answer
    B. 22.7 square yards
  • 27. 

    Use the figure below to find the value of x. x = ________ degrees

    Correct Answer
    26
  • 28. 

    A carpenter has a board with the given dimensions. If he cuts out the two circles, as shown, how much board will be left? Round your answer to the nearest tenth. There will be _______ square inches left.

    Correct Answer
    15.5
    Explanation
    After cutting out the two circles, the remaining board will have an area of 15.5 square inches.

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  • Current Version
  • Mar 17, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 28, 2014
    Quiz Created by
    Victoriastephens
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