Pythagoras is planting a rose garden in the center of his rectangular yard, which is 20 feet long and 8 feet wide. He wants to dig up an area in the shape of an equilateral triangle with sides 5 feet each. After he digs up the rose-bed section, approximately how much grass will be left? Round to the nearest foot.

The remaining area that the grass will cover will be given by:

Area=[area of rectangle]-[area of the triangle]

area of rectangle will be:

A1=length*width

=20*8

=160 square feet

The area of the triangle will be:

A2=1/2absin theta

since the triangle is equilateral, all the angles are equal and the size of each angle is 60°. Thus the area will be:

A2=1/2*5*5sin 60

=18.3

thus the remaining area of the grass will be:

Area=160-18.3

=149.7 square feet