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.
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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