Answer:
D 36.6
Step-by-step explanation:
Here, there is a triangle inscribed inside of a semicircle where the triangle is unshaded and the remained of the semicircle is shaded and we want to find the area of that shaded untouched area of the semicircle.
To do so we must find the area of the two shapes individually and then subtract the area of the triangle from the area of the semi circle as the triangle is what is uncovering the semicircle.
Finding the area of the semicircle
Area of a semicircle = (πr²)/2 where r = radius
Here we are given the diameter of the semicircle which is 13cm. We can easily convert the diameter to radius by dividing it by 2 as the radius is equal to half the diameter
Radius = 1/2 diameter , so radius = 13 / 2 = 6.5cm
We have A = πr²/2
==> plug in radius or r = 6.5
A = π(6.5)²/2
==> simplify exponent
A = π(42.25)/2
==> multiply π and 42.25 ( note that π = 3.14 approximately
A = 132.665/2
==> divide 132.665 by 2
A = 66.366
So the area of the semicircle is 66.366cm²
Finding the area of the triangle
The area of a triangle can be calculated by dividing the product of the base length and height ( formula = bh / 2 where b = base length and h = height )
Here the base length appears to be 5cm and the height appears to be 12cm so b = 5 and h = 12
So we have A = bh/2
==> plug in b = 5 and h = 12
A = (12)(5)/2
==> multiply 12 and 5
A = 60 / 2
==> divide 60 by 2
A = 30
So the area of the triangle is 30cm²
Subtracting the area of the triangle from the area of the semicircle
Finally to find the area of the shaded region we subtract the area of the triangle from the area of the semicircle
We have area of triangle = 30cm² and area of semicircle = 66.366
So area of shaded region = 66.366 - 30 = 36.366
D , 36.6 is closest to our answer therefore the answer is D
