Question

Help! Find the area of the figure above... please explain!

Answer 1

You have to break it up into individual pieces.

First, find the area of the inner triangle. The area of a triable is 1/2(base•height). Since there's 2 right triangles, you can just do (base•height).

Triangle area=(5•12)=60

To find the area of the bottom semicircle, use the formula for area of a circle and then divide by 2 since it's half a circle. A=(pi)r^2. The radius in this case is 5 (half of 10.)

Area of bottom circle=25pi/2

To find the area of the remaining circle parts, since both the half-circles are equal, we can just find the area of one whole circle with those dimensions.

A=(6.5)^2(pi)

The total area of the whole figure will be those 3 components added together.

A=25pi/2+42.25pi+60 meters squared

Answer 2

Let's find the area of the top two semi-circles. 
First we need the radius.
r = radius d = diameter a = area
r = d/2
r = 13/2
r = 6.5
a = r²
a = 6.5²
a = 42.25
Now, if there was only one semi-circle we would divide that in half. But there are two, so the area of both semi-circles is 42.25.

Now for the left triangle. 
base = b height = h
a = b · h · 0.5
a = 5 · 12 · 0.5
a = 60 · 0.5
a = 30
Same for the triangle on the right. 30 + 30 = 60.

Now for the bottom semi circle.
r = d/2
r = 10/2
r = 5
a = r²
a = 5²
a = 25
Now since there's only one semi-circle this time we divide by two. 25/2=12.5

Now we add: 12.5 + 60 + 42.25 = 114.75

The answer is 114.75. 

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