7 grade math Area of compound figures with triangles, semicircles, and quarter circles

area = 250.04 km^2

Step-by-step explanation:

In the image, we have the next figures.

One quart of a circle, with radius R = 12km

A large rectangle, with length L = 13km and width = 9 km

(to find the width of this rectangle, look at the bottom, we have a part of 5km, and then we have the small rectangle with a width of 4km, then 4km + 5km = 9km)

And finally, a smaller rectangle with length L = 5km and width W = 4km

Now, the general rules for each figure are:

The area of a circle of radius R, is

A = pi*R^2

with pi = 3.14

Here we have the fourth part of a circle with a radius R = 12km

Then the area of that part is:

area = (1/4)*3.14*(12km)^2 = 113.04 km^2

And the area of a rectangle of length L and width W is:

A = W*L

Then, the area of the larger rectangle is:

A' = 9km*13km = 117 km^2

And the area of the smaller rectangle is:

A'' = 4km*5km = 20km^2

The complete area of the figure is:

area = A + A' + A'' =  113.04 km^2 +  117 km^2 + 20km^2 = 250.04 km^2

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