Question

Lin is making a window covering for a window that has the shape of a half circle on top of a square of side length 3 feet. How much fabric does she need

Answer 1

Lin needs 12.53 square feet of fabric

Explanation:

we know that

The area of the window covering is equal to the area of the square plus the area of semicircle

step 1

Find the area of the square

The area of the square is equal to

`A_1=b^(2)`

where

b is the length side of the square

we have

`b=3\ ft`

substitute

`A_1=3^(2)=9\ ft^2`

step 2

Find the area of semicircle

The area of semicircle is equal to

`A_2=(1)/(2)\pi r^(2)`

The length side of the square is equal to the diameter of semicircle

so

`r=3/2=1.5\ ft` ----> the radius is half the diameter

assume

`\pi =3.14`

substitute

`A_2=(1)/(2)(3.14)(1.5)^(2)`

`A_2=3.53\ ft^2`

Adds the areas

`A=A_1+A_2`

`A=9+3.53=12.53\ ft^2`

therefore

Lin needs 12.53 square feet of fabric