a square table 4 feet on each side has two drop leaves, each a semicircle 4 feet in diameter. find the area of the table with and without the drop leaves.

troller27
Apr 6, 2017

#1**+3 **

Here is a top down view of the table.

The purple semicirles are the leaves. The blue square is the table.

As you can see, the table can be split up into two shapes: a square and a circle.

The area *without *the drop leaves = the area of the square.

The area *with* the drop leaves = the area of the square + the area of the circle.

So... let's start by finding the area of each shape.

__the area of the square __= length * width = 4 * 4 __= 16 sq. ft.__

__the area of the circle __= π * radius^{2} = π * (4/2)^{2} = π * 2^{2} __= 4π sq. ft.__

So..

**The area without the drop leaves** = the area of the square

**The area with the drop leaves** = the area of the square + the area of the circle.

hectictar
Apr 7, 2017