Download Name - Mr. Nickels

Name:_________________________
Math A Year 2 Lab #32
Mr. Nickels
Quadratic Area Problems
1
Express both the perimeter and the area of the rectangle shown in the accompanying diagram as
polynomials in simplest form.
2
In the figure below, the large rectangle, ABCD, is divided into four smaller rectangles. The area of
rectangle AEHG = 5x, the area of rectangle GHFB = 2 x 2 , the area of rectangle HJCF = 6x, segment
AG = 5, and segment AE = x.
a Find the area of the shaded region.
b Write an expression for the area of the rectangle ABCD in terms of x.
3
In the accompanying figure, ACDH and BCEF are rectangles, AH=2, GH=3, GF=4, and FE=5.
What is the area of BCDG?
(1) 6
(2) 8
(3) 10
(4) 20
4
Jack is building a rectangular dog pen that he wishes to enclose. The width of the pen is 2 yards
less than the length. If the area of the dog pen is 15 square yards, how many yards of fencing
would he need to completely enclose the pen?
5
The area of the rectangular playground enclosure at South School is 500 square meters. The length
of the playground is 5 meters longer than the width. Find the dimensions of the playground, in
meters.
6
Javon’s homework is to determine the dimensions of his rectangular backyard. He knows that the
length is 10 feet more than the width, and the total area is 144 square feet. Write an equation that
Javon could use to solve this problem. Then find the dimensions, in feet, of his backyard.
7
A rectangular park is three blocks longer than it is wide. The area of the park is 40 square blocks.
If w represents the width, write an equation in terms of w for the area of the park. Find the length
and the width of the park.
8
Mr. Santana wants to carpet exactly half of his rectangular living room. He knows that the
perimeter of the room is 96 feet and that the length of the room is 6 feet longer than the width.
How many square feet of carpeting does Mr. Santana need?
9
Determine the area, in square feet, of the smallest square that can contain a circle with a radius
of 8 feet.