OAR OAR Math Skills: Geometry Questions and Answers 2

Question 1

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is its surface area?

Accepted Answer

158 sq cm

Answer

Surface area = 2(lw + lh + wh) = 2(40 + 24 + 15) = 2(79) = 158 sq cm.

Question 2

Two similar triangles have a scale factor of 3:5. If the area of the smaller triangle is 27 sq in, what is the area of the larger triangle?

Accepted Answer

75 sq in

Answer

Area ratio equals the square of the scale factor: (3/5)^2 = 9/25, so 27/x = 9/25, giving x = 75 sq in.

Question 3

What is the measure of each interior angle of a regular octagon?

Accepted Answer

135 degrees

Answer

Interior angle = (n-2) x 180 / n = (8-2) x 180 / 8 = 1080 / 8 = 135 degrees.

Question 4

A chord is 6 cm from the center of a circle with radius 10 cm. What is the length of the chord?

Accepted Answer

16 cm

Answer

Half the chord = sqrt(10^2 - 6^2) = sqrt(64) = 8, so the full chord = 16 cm.

Question 5

If the diagonal of a square is 10 units, what is the area of the square?

Accepted Answer

50 sq units

Answer

Area of a square given its diagonal d is d^2/2 = 100/2 = 50 sq units.

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