Question

1. Find the area of the regular polygon to the nearest tenth.

square with a radius of 13 m

A) 344 m²
B) 676 m²
C) 169 m²
D) 338 m²

2. Find the area of the triangle give the answer to the nearest tenth. The drawing may not be to scale.

(see picture attached)

A) 47.4 cm²
B) 94.8 cm²
C) 7.5 cm²
D) 303.1 cm²

Answer 1

1. D) 338 m²
2. A) 47.4 cm²

Explanation:

You can use the same formula in each case. The area of a triangle with sides "a" and "b" separated by angle α is ...

A = (1/2)ab·sin(α)

1. The area of the square is 4 times the area of the right triangle whose legs are radii of the square:

square area = 4·(1/2)·(13 m)(13 m)sin(90°) = 2·(13 m)² = 338 m²

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2. The area is ...

A = (1/2)(8 cm)(12 cm)sin(81°) ≈ 47.4 cm²

For this one, you don't need to work out the answer in detail. You know it will be less than, but nearly, 48 cm², which is half the product of the side lengths.