Question

Find the area and circumference of the figure below.

Answer 1

Answer:

162.12385 cubic inches

Step-by-step explanation:

Assuming finding the area and circumference of the shaded area.

Triangle with 3 sides and 90 degrees on one side, we can use the Pythagorean Theorem to solve for the missing side.

Pythag. Theorem says

a^2 + b^2 = c^2

//a and b are the 2 small sides touching to the 90 degree angle

//^2 means squared, or the number multiplied by itself

(16)^2 +(30)^2 = c^2

16x16 + 30x30 = c^2

256 + 900 = c^2

1156 = c^2

Take the square root of both sides to get rid of (^2) from the right side of the equation.

sqrt(1156) = sqrt(c^2)

34 = c

So the longest side is 34 inches.

Coincidentally, this is the diameter of the Half Circle.

The radius = (diameter/2) = 34/2 = 16 inches

radius = 16 in.

Circumference of a Circle formula:

C = 2*pi*r; pi=3.14; r = radius

But this is a half circle, so C = pi*r = 3.14*16 = 50.2654

Now to find the area its a little more work.

Area of shaded part is equal to

Area of half circle   minus    area of triangle

Area of Circle: pi*r^2

-->since half circle: Area of half circle is: (pi*r^2)/2

Area of triangle: (base*height)/2: (16*30)/2

A of circle - A of triangle

(3.14*16^2)/2 - (16*30)/2

Area of shaded region = 162.12385