Answer:
#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)
<em>12.5 squared is 156.25.</em>
1/2(3.14 * 156.25)
<em>Multiply 3.14 by 156.25 to get 490.625.</em>
1/2(490.625)
<em>Divide 490.625 by 2 to get 245.3125.</em>
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)
<em>Multiply 12.5 by 25 to get 312.5.</em>
312.5 + 1/2(31 * 12.5)
<em>Multiply 31 by 12.5 to get 387.5.</em>
312.5 + 1/2(387.5)
<em>Multiply 1/2 by 387.5 to get 193.75</em>
312.5 + 193.75
<em>Add 312.5 and 193.75 to get 506.25.</em>
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)
<em>Multiply 40 by 27 to get 1080.</em>
1/2(1080)
<em>Multiply 1/2 by 1080.</em>
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.
