Find the area explain how you got your answer​

189.27in^2

Step-by-step explanation:

Area of the rectangle is l*w

15*10= 150

Area of the circle is π r^2

We don't have radius but we have diameter so 10/2 =5

so A= π 5^2

78.53982, but we need half that since its only half a circle.

78.53982/2 = 39.26991

39.26991 + 150 = 189.26991

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

there are infinitely many solutions.