Question

Find the area of the following figure: 11in 10in

Answer 1

(no simplification) = 55 + (25
`\pi`/2) in^2

(with simplification) = (110 + 25
`\pi`)/2 in^2

(with pi rounded to 3.14) = 94.25 in^2

Explanation:

Let's start with the easier shape, the triangle. The formula for area of a triangle is 1/2(base)(height). Since at the far right we have 10 in, we can apply that to the triangle to get the base = 10 inches. The height is given as 11 inches so we can then calculate the area which is 55 in^2.

Then, the circle. We know that area of a whole circle =
`\pi r^(2)`. Since we know that a semicircle is 1/2 of a full circle, we can find the area of the entire circle then divide it by 2.

It gives the diameter as 10, divide that by 2 to get the radius. r=5. Plug 5 into the equation of
`\pi r^(2)` and you get 25
`\pi`. Divide that by 2 to get 25
`\pi`/2.

Add the triangle and the semicircle areas.

(no simplification) = 55 + (25
`\pi`/2) in^2

(with simplification) = (110 + 25
`\pi`)/2 in^2

(with pi rounded to 3.14) = 94.25 in^2