1. Find the area of the composite figure to the nearest hundredth. 2. Find the area of the shaded region to the nearest tenth.

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

12.5 squared is 156.25.

1/2(3.14 * 156.25)

Multiply 3.14 by 156.25 to get 490.625.

1/2(490.625)

Divide 490.625 by 2 to get 245.3125.

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

Multiply 12.5 by 25 to get 312.5.

312.5 + 1/2(31 * 12.5)

Multiply 31 by 12.5 to get 387.5.

312.5 + 1/2(387.5)

Multiply 1/2 by 387.5 to get 193.75

312.5 + 193.75

Add 312.5 and 193.75 to get 506.25.

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

Multiply 40 by 27 to get 1080.

1/2(1080)

Multiply 1/2 by 1080.

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².