Question

A rectangular paperboard measuring

26 in long and 20 in
wide has a semicircle cut out of it.

Find the area of the paperboard that remains. Use the value 3.14
for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

See below.

Explanation:

Find the area of the rectangle using A = l*w = 26*20 = 520.

Now find the area of the semi circle using A = 1/2 πr². Since the instructions do not say the diameter of the semi circle assume it is 20 or 26.

If it is 20: r = 10 and the area is A = 1/2 π10²=50π = 157.

If it is 26: r = 13 and the area is A = 1/2π13² = (84.5)π = 265.33.

The area of the paperboard that remains will be the area of the rectangle minus the area of the semi circle.

If the diameter of the semi circle is 20 then 520 - 157 = 363.

If the diameter of the semi circle is 26 then 520 - 254.67.

Answer 2

The remaining area of the paperboard is 363 square inches.

Explanation:

The length of the rectangular board = 26 inches

The width of the rectangular board = 20 inches.

Now, the area of the board =
`26*20=520` square inches

Now, a semicircle has been cut out of it.

Let is assume that the diameter of the semicircle be 20 inches.

So, radius will be = 10 inches

Area of semicircle is =
`(1)/(2) \pi r{2}`

So, we get : Area =
`(1)/(2)*3.14*10*10`

= 157 square inches.

Now after cutting the semi circle, the area remained =
`520-157=363` square inches.

Therefore, the remaining area of the paperboard is 363 square inches.