Areas of 2-Dimensional Figures

Do you know the area of the NBA court? It could be determined by the formula A = lw. To find the area of a region, cover it with copies of a simple region. The area is the number of copies that are needed. For example, the rectangle below with length 5 and width 7 can be covered with 35 squares with each side 1 unit in length (shown as filled). 5*7 rectangle with 1*1 unit square So we say that the area is 35 square units or 35 units2. There are 5 rows and 7 columns. These numbers are the dimensions of the rectangle. The number of squares in the rectangle is the product of its dimensions. The areas of all 2-Dimensional shapes follow the area postulate:

Area Postulate:
a. Uniqueness Property: Given a unit region, every polygonal region has a unique area.
b. Rectangle Formula: The area of a rectangle with dimensions l and w is l*w.
c. Congruence Property: Congruent (same) figures have the same area.
d. Additive Property: The area of the union (sum) of two nonoverlapping regions is the sum of the areas of the regions.

The area of a circle is expressed by the formula ¶r2, (What's ¶?) where r is the radius of the circle (marked as r in the picture below). circle with radius r

Sample Problem

Given: The NBA court is a 50*94 rectangle, the small center circle has a radius of 2 ft.
Find: The percent of the court that is taken up by 1/2 of the center circle.

Plan: 1) Find area of court, 2) Find area of circle, 3) Find area of 1/2 of the circle, 4) Find the percentage of court taken up by 1/2 of the circle

Solution:
1) Find area of court: since we know by the area postulate that the area of a rectangle is length*width, we multiply the length and width (50*94) and arrive at the area of 4700 sq. ft.
2) Find area of circle: since we know by the circle area formula that the area of a circle is ¶r2, we substitute the knowns (¶=3.14, r=2) to get the formula 3.14*2*2. We solve the expression and arrive at the answer of 12.56 sq. ft.
3) Find area of 1/2 of the circle: to find 1/2 of an area, we simply divide it by 2. Thus, 12.56/2=6.28 sq. ft., our answer for 1/2 of the circle.
4) Find the percentage of the court taken up by 1/2 of the circle: to do this, we must divide the part (1/2 of the area of the circle, 6.28 ft2) by the total (area of the court, 4700 ft2). Once we do this, we arrive at the answer of .0013 (6.28/4700). To convert that to percent, we must multiply it by 100. Now, our answer is .13%.

Finale: The final answer is: the area of the center circle in the middle of the NBA court is .13% of that court.

Great, let me try some problems myself!

1. A home owner wants to carpet his living room. The carpet is $18.95 a square yard. How much will it cost to carpet the living room that is 9 feet by 12 feet without tax and any other charge such as installation? $

2. Find the area of the polygon with vertices (0,0), (0,10), (10,10), (10,0) units2

3. A rectangle with an area of 50 square yards has a length of 100 yards. What is the width of the rectangle? yards

4. A desk is 24" by 12". What is its area in square inches? square inches

5. How many square inches are in a square foot? in2

Stumped? Take a look at the answer key!

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