Question

Yuki bought a drop–leaf kitchen table. The rectangular part of the table is a 2–by–3–foot rectangle with a semicircle at each end, as shown.

Answer 1

`(a)\ Area = 13.0695`

`(b)\ Area = 26.139`

Explanation:

Given

The attached image

Solving (a): The area (one side up)

This is calculated as:

Area= Area of semicircle + Area of rectangle

So, we have:

`Area = \pi r^2 + l *w`

Where:

`l,w =2,3` --- the rectangle dimension

`d = 3` --- the diameter of the semicircle

So, we have:

`Area = \pi * (3/2)^2 + 2 * 3`

`Area = \pi * 2.25 + 6`

`Area = 2.25\pi + 6`

`Area = 2.25*3.142 + 6`

`Area = 13.0695`

Solving (b): Area when both leaves are up.

Simply multiply the area in (a) by 2

`Area = 2 * 13.0695`

`Area = 26.139`