Question

Question 1 (1 point)

A decorator is wallpapering a wall with a circular window of diameter 1.00 m.What is the
area of the wall in square feet? (1 m - 3.2808 feet)
3

Answer 1

95.875
`ft^(2)`

Explanation:

1.) Calculate the area of the trapezoid

A(trapezoid) = (1/2)*(base1 + base2)*h = (1/2)*(2.6+3.6)*3 = (1/2)*6.2*3 = 9.3

2.) Calculate the area of the circle

radius = (1/2)*(diameter) = (1/2)*1 = 0.5

A(circle) = (1/2)*
`\pi`*
`r^(2)` = (1/2)*
`\pi`*(
`0.5^(2)`) = (1/2)*
`\pi`*0.25 = 0.125*
`\pi` = 0.392699

3.) Because the area of the circle is not included in the wall, subtract the area of the circle from the area of the trapezoid:

A(trapezoid)-A(circle) = 9.3-0.392699 = 8.9073
`m^(2)`

4.) Convert to
`ft^(2)`:

Because 3.2808 feet are in a meter and the unit of the answer is in
`m^(2)`, we need to multiply the answer by (
`3.2808^(2)`) to get to
`ft^(2)`.

8.9073*(
`3.2808^(2)`) = 8.9073*10.7636 = 95.875
`ft^(2)`