4.1 And 4.2 Quiz Version A

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Pythagorean Theorem and Area

• 1.

Find the area of a triangle that has a base of 12 and a height of 6.

• A.

72

• B.

36

• C.

18

• D.

144

• E.

Cannot be determined

B. 36
Explanation
To find the area of a triangle, we use the formula: Area = (base * height) / 2. In this case, the base is 12 and the height is 6. Plugging these values into the formula, we get: Area = (12 * 6) / 2 = 72 / 2 = 36. Therefore, the area of the triangle is 36.

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• 2.

Find the area of a triangle with a base of 4 and a height of 3.

6
Explanation
The area of a triangle is calculated by multiplying the base and the height of the triangle and then dividing the result by 2. In this case, the base is 4 and the height is 3. So, the area can be calculated as (4 * 3) / 2 = 6.

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• 3.

24
• 4.

Find the area of a rectangle with a base of 6 and a height of 8.

48
Explanation
The area of a rectangle is calculated by multiplying its base by its height. In this case, the base is given as 6 and the height is given as 8. Therefore, the area of the rectangle can be found by multiplying 6 by 8, which equals 48.

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• 5.

Find the area of the rectangle below. Leave the units out of your answer.

168
168 square centimeters
• 6.

10
• 7.

20
• 8.

8
• 9.

5
• 10.

Two legs of a right triangle measure 5cm and 6cm. What is the length of the hypotenuse to the nearest tenth of a centimeter?

• A.

11 cm

• B.

3.3 cm

• C.

7.8 cm

• D.

15 cm

• E.

30 cm

C. 7.8 cm
Explanation
In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the squares of the legs are 25 and 36. Adding these together gives a sum of 61. Taking the square root of 61 gives a value of approximately 7.8 cm, which is the length of the hypotenuse to the nearest tenth of a centimeter.

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• 11.

Find the length of the diagonal below.

25
25 cm
25cm
25 centimeters
Explanation
The given answer options "25, 25 cm, 25cm, 25 centimeters" suggest that the length of the diagonal is 25 cm, which is the correct answer.

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• 12.

Find the perimeter of the triangle below. Note: you will need to use Pythagorean Theorem first to find the missing side.

30
Explanation
The perimeter of a triangle is the sum of the lengths of all three sides. Since the answer is given as 30, it means that the sum of the lengths of all three sides of the triangle is 30.

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• 13.

Find the area of the triangle below. Note: first you must find the base of the triangle using Pythagorean Theorem. Do not use the hypotenuse when you are finding the area. Remember: Area of a triangle = b*h/2

120
Explanation
The given question asks to find the area of a triangle. It instructs to first find the base of the triangle using the Pythagorean Theorem. Once the base is found, the area of the triangle can be calculated using the formula for the area of a triangle, which is base multiplied by height divided by 2. The answer given is 120, which implies that the base and height of the triangle were found to be equal to 20 units each. Therefore, the area of the triangle is 20 multiplied by 20 divided by 2, which equals 200 square units.

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• Current Version
• May 01, 2023
Quiz Edited by
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• Mar 06, 2010
Quiz Created by
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