Lesson 9 Instruction, page 2

Pre-Test		Post-Test
Q&A	Figuring Out Area	Q&A

Area Formulas
CA GR4 NS 1.4, CA GR4 MG 1.1, CA GR5 MG 1.1 & 1.2, 1.4, CA GR6 AF 3.1 & 3.2, CA GR6 MG 1.1, CA GR7 MG 2.1

Area is the measure of square units on a surface. Generally (for parallelograms) the area of a surface is found by multiplying the base dimension times the height dimension. Area measurements will always be in square units - square feet, square yards, square miles, etc. To find the area of a rectangle (or a square):

	A = bh
	where	b = length of the base
		h = height
	Example:	A = bh
		A = 6 ft (b) x 4 ft. (h)
		A = 24 square feet

Figure 4

	Example:	A = bh
		A= 5 ft.(b) x 5 ft. (h)
		A = 25 square feet

Figure 5

To find the area of a parallelogram, the same formula holds true:

	A = bh
	Example:	A = bh
		A = 6 ft. (b) x 3 ft. (h)
		A = 18 square feet

Figure 6

Notice, however, that the height of a parallelogram is not the same dimension as any of its sides. Here, and normally in all measurements, height refers to the distance of a line which is perpendicular to the base. Look at Figure 6 and you can see why the same formula will work for a rectangle and a parallelogram.

A trapezoid can also be compared to a rectangle. When it is, as in Figure 7, you can see why the formula to find the area of a trapezoid is:

It is because you must find the average of the lengths (bases) and multiply that figure by the height. So the area of X in Figure 7 would be:
	Figure 7

Actually, the formula for finding the area of a triangle is similar to those for finding the area of a rectangle and related figures. How does a triangle compare to a rectangle and related figures? To find the area of a triangle, you still multiply the base times the height, but you take one-half the result since a triangle can be considered as a rectangle or parallelogram cut in half.

To find the area of a triangle:

(See Figure 8)

Figure 8

To find the area of a circle, square the radius and multiply the result by Pi (3.1416)
(CA GR6 MG 1.1):

	Example:	A = r²
		A = (3.1416) (5 ft.) (5 ft.)
		A= (3.1416) (25 square feet)
		A = 78.5400 square feet or 78.54 sq. ft.

Figure 10

If the dimension given in the circle is the diameter, remember that the dimension's twice the radius, so you take one-half of it and proceed as before:

	Example:	A = r²
		A = (3.1416) (4 ft.)(4 ft.)
		A= (3.1416) (16 square feet)
		A = 50.2656 square feet or 50.27 sq. ft.

Now, let's stop and take Practice Exercise 9-2, Practice Exercise 9-2-a(top)

For more instruction on finding the area of squares and rectangles including examples and Practice Exercises click on the link below: www.mathgoodies.com/lessons/vol1/area_rectangle.html

For additional instruction on finding the area of parallelograms including examples and Practice Exercises click on the link below:
www.mathgoodies.com/lessons/vol1/area_parallelogram.html

Click on the following link below for some Practice Exercises for both Perimeter and Area of polygons:
www.mathgoodies.com/lessons/vol1/challenge_vol1.html

Note: Step by step solutions to most of these Practice Exercises are provided at the end of the instruction section by clicking on the math link there.

Next Page: Three Dimensional Shapes and Surface Area