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.

Please go to the link below for additional instruction for this topic included on the HSEE:

Area of Polygons & Circles:
http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=farea

Next Page: Three Dimensional Shapes and Surface Area