1.
Jonathan has created a new pencil that is in the shape of a triangle. He is trying to develop the best way to market this invention. His pencil seems to be a bit awkward and no sides are the same. He calls it the Scalene Pencil by Big "J". His triangle has side lengths of 3 cm., 1.6 cm., and 2.2 cm. What is the perimeter of his new invention?
Correct Answer
B. 6.8 cm.
Explanation
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the triangle has side lengths of 3 cm, 1.6 cm, and 2.2 cm. Adding these lengths together, we get a sum of 6.8 cm. Therefore, the perimeter of Jonathan's new invention, the Scalene Pencil, is 6.8 cm.
2.
A triangular field has a base of 14 m and a height of 18m. What is the area of the field.
Correct Answer
C. 126 square meters
Explanation
The area of a triangle is calculated by multiplying the base by the height and dividing the result by 2. In this case, the base is 14 m and the height is 18 m. So, the area of the triangular field would be (14 * 18) / 2 = 126 square meters.
3.
If the base of a rectangle is 25 m and the area is 175 m^{2}, what is the height of the rectangle?
Correct Answer
D. 7 m
Explanation
The area of a rectangle is calculated by multiplying its base by its height. In this case, we know that the base is 25 m and the area is 175 m2. To find the height, we can divide the area by the base. 175 m2 divided by 25 m equals 7 m. Therefore, the height of the rectangle is 7 m.
4.
Classify this triangle. Choose all names that would apply
Correct Answer(s)
A. Isosceles
C. Right
Explanation
The given triangle can be classified as isosceles because it has at least two sides that are equal in length. It can also be classified as right because it has one angle that measures 90 degrees.
5.
Classify the triangle above
Correct Answer
D. Obtuse Sclene
Explanation
The triangle is classified as an Obtuse Scalene triangle because it has one angle that measures more than 90 degrees (obtuse) and all three sides are of different lengths (scalene).
6.
Find the missing angle
Correct Answer
D. 70
Explanation
The missing angle can be found by subtracting the sum of the given angles from 180 degrees, since the sum of the angles in a triangle is always 180 degrees. In this case, 40 + 110 + 80 = 230, so the missing angle can be found by subtracting 230 from 180, resulting in 70 degrees.
7.
Classify the triangle.
Correct Answer
C. Acute Isosceles
Explanation
The given answer, "Acute Isosceles," suggests that the triangle being classified is both acute and isosceles. An acute triangle is a triangle in which all three angles are less than 90 degrees. An isosceles triangle is a triangle with at least two sides of equal length. Therefore, the answer implies that the triangle in question has two equal sides and all three angles are less than 90 degrees.
8.
A triangle has the following angle measurements: 62 and 57. Classify this triangle by its sides and angles.
Correct Answer
D. Acute Scalene
Explanation
Based on the given angle measurements of 62 and 57, we can determine that this triangle does not have any angle measuring 90 degrees or more, making it an acute triangle. Additionally, since none of the sides have equal lengths, it is a scalene triangle. Therefore, the correct classification for this triangle is "Acute Scalene".
9.
A triangle has the following angle measurements: 58 and 73. What is the missing angle measurement?
Correct Answer
D. 49
Explanation
Since a triangle has a total of 180 degrees, we can find the missing angle by subtracting the sum of the given angles (58 + 73 = 131) from 180. Therefore, the missing angle measurement is 49 degrees.
10.
Choose the classifications that fit the triangle above.
Correct Answer(s)
A. Obtuse
D. Isosceles
Explanation
The triangle in the question has one angle that is greater than 90 degrees, making it obtuse. Additionally, it has two sides that are equal in length, making it isosceles.
11.
An equilateral triangle can be classified as an isosceles.
Correct Answer
A. True
Explanation
In order to be classified as an isosceles, it must have AT LEAST 2 congruent sides. An equilateral triangle has 3 congruent sides.
12.
Dr. McLaughlin designed a new bulletin board in the shape of a parallelogram. The base of the board is 471.5 cm., Ā the height is 21.3 cm., and the side length is 24 cm. What is the perimeter of the McLaughlin B-Board?Ā
Correct Answer
A. 991 cm.
Explanation
The perimeter of a parallelogram can be found by adding up the lengths of all its sides. In this case, the base and the opposite side of the parallelogram are equal in length, so the perimeter is twice the length of the base plus twice the length of the side. Therefore, the perimeter is 2(471.5 cm) + 2(24 cm) = 943 cm + 48 cm = 991 cm.
13.
The area of a trapezoid base 1= 12, base 2= 15, height= 4 is?
Correct Answer
D. 54 square units
Explanation
the area formula for a trapezoid = 1/2H(b1+b2)
14.
Why might you want to measure the area?
Correct Answer
C. All of the above
Explanation
Measuring the area is important because it allows you to determine the amount of carpet needed for your home, which is essential for estimating the cost. Additionally, measuring the area helps in determining the amount of grass seed required for your yard, ensuring that you buy the right quantity. Therefore, the correct answer is "All of the above" as both options are valid reasons for wanting to measure the area.
15.
Give all the names that apply to this quadrilateral.
Correct Answer
B. Parallelogram, Rhombus
Explanation
The given quadrilateral can be classified as a parallelogram because opposite sides are parallel. Additionally, it can be classified as a rhombus because all four sides are equal in length. However, it cannot be classified as a rectangle or square because the angles are not all 90 degrees.
16.
Give all the names that apply to this quadrilateral.
Correct Answer
C. Parallelogram, Rectangle
Explanation
The given quadrilateral can be classified as a parallelogram because opposite sides are parallel. Additionally, it can also be classified as a rectangle because all angles are right angles.
17.
Megan wants to build a fence around her vegetable garden. Her garden is 8 ft. long and 3.25 ft wide. How much fencing will Megan need for her wonderful garden?
Correct Answer
B. 22.50 ft
Explanation
Megan wants to build a fence around her vegetable garden, which is 8 ft long and 3.25 ft wide. To calculate the amount of fencing she needs, we add up the lengths of all four sides of the garden. The two lengths are 8 ft each, and the two widths are 3.25 ft each. Adding these together gives us a total of 22.50 ft of fencing needed.
18.
What is the height of a rectangle with perimeter 126.6 mm and base length 40.4 mm?**Draw a picture to help**
Correct Answer
C. 22.9 mm
Explanation
The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter is given as 126.6 mm. We are also given the length of the base as 40.4 mm. To find the height, we need to subtract the length of the base from the perimeter, and then divide the result by 2 (since the other two sides are equal in length). So, (126.6 - 40.4) / 2 = 86.2 / 2 = 43.1 mm. Therefore, the height of the rectangle is 43.1 mm.
19.
Calculate the area of the figure below
Correct Answer
C. 120
Explanation
The figure is not described or shown in the question, so it is not possible to calculate its area. Therefore, the explanation for the given answer (120) is not available.
20.
Calculate the area of the figure below
Correct Answer
B. 27
21.
Find the area of a triangle with a height that is 5 m and half of the base is 9m.
Correct Answer
45 meters squared
45
45m2
45 meter squared
Explanation
The area of a triangle can be calculated using the formula: Area = (1/2) * base * height. In this case, the height is given as 5m and half of the base is given as 9m. Therefore, the full base would be 2 * 9m = 18m. Substituting these values into the formula, we get: Area = (1/2) * 18m * 5m = 45m^2. So, the correct answer is 45 meters squared.
22.
Arusha needs to buy fertilizer to spread in her garden. The garden is 20 feet by 15 feet. How much fertilizer will she need to cover her garden?
Correct Answer
300 feet squared
300
300 ft2
300 ft squared
Explanation
Arusha needs to buy fertilizer to cover her garden, which is 20 feet by 15 feet. To find the area of the garden, we multiply the length by the width. So, 20 feet multiplied by 15 feet equals 300 square feet. Therefore, Arusha will need 300 feet squared of fertilizer to cover her garden.