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Measurement, Perimeter, and Area for CBEST Exam Study Guide (page 3)

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Updated on Mar 29, 2011

1. This problem can be solved at least two ways. You can turn the ounces into of a pound and multiply 1.60 × . Alternately, you can multiply 1.60 by 3, then multiply 1.60 by and add the two together. Choice c is the answer.
2. When subtracting 8 inches from 3 inches, borrow one foot from the 6 feet. Add 12 inches to the 3 inches to get 15"; 15 – 8 = 7 and 5 – 2 is 3. The answer is choice c.
3. The trick here is to realize that the 10' dowels are really only good for 9' since the scouts need 3' pieces. The scouts need a total of 48': 8 × 2 × 3 = 48. Five dowels would be good for only 45', but six dowels would provide more than enough (54'). The answer is choice e.
4. There are 128 ounces in a gallon. 128 – 1 oz. = 127 oz. 127 – 8 oz. (1 cup) = 119 oz. 119 – 32 oz. (1 qt.) = 87 oz. There are 16 ounces in 1 pint, so = pt. The correct answer is choice b.
5. The easiest way to do this one is to change everything to feet to begin with. 5 yards is 15 feet × = 6.25. The answer is choice a.
6. Multiply 20 × 20 to get the total time. Convert the answer, 400, from minutes to hours by dividing by 60, to get , or 6 hours 40 minutes. From noon to 2 P.M. is 2 hours. Subtract the remaining 4 hours and 40 minutes from 12 noon; think of 12 noon as 11 plus 60 minutes. 11:60 – 4:40 = 7:20 A.M. The correct answer is choice d.

Perimeter and Area Formulas

Following are important formulas you need to know.

Rectangle

Area: length times width (A = lw). The length of one side times the length of the other side tells you how much space is inside.
Perimeter: 2 length + 2 width (2l + 2w). To measure all the way around something rectangular, you need to include 2 lengths and 2 widths—that's all four sides.

Square

Measuring the area and perimeter of a square is the same as measuring the area and perimeter of a rectangle, only the length and width are the same measurement.

Area: side × side
Perimeter: side × 4

Triangle

Remember that a triangle is half a rectangle.

Area:b × h. Multiply the height and the base. Since the area of the triangle is half the area of the rectangle, divide by 2. Note: The height of a triangle is not always one of the sides. For example, in triangle ABC, is not the height, is the height. is the base. To find the area, ignore all the numbers but the base and the height. The base can be found by adding 4 and 8: 4 + 8 = 12. The height is 5. × 5 × 12 = , or 30.

Perimeter: Add the sides all around: 12 + 6 + 9 = 27.

Circle

The diameter of a circle goes from one point on the circle through the center, and all the way to another point on the circle. The length of the radius (r) is half of the diameter. When working with π, consider the following: The symbol π is usually found in the answers so that you don't have to worry about converting it to a number. But if π is not found in the answers, and the question calls for an approximate answer, you can estimate by substituting 3 for π. The question may also tell you to use or 3.14.

Area: πr2. Square the radius and look at the answers. If π is not found in the answers, multiply by 3. In the previous example, A = π42or 16π.

Circumference: 2πr. Circumference is to a circle what perimeter is to a rectangle. Multiply the radius by 2 and look for the answers. If π is not in the answer choices, multiply by 3. In the example above, the circumference is 2π4, or 8π.

Other Areas

Cut the figure into pieces, find the area of each, and add. If you're asked to find the area of a figure with a piece cut out of it, find the area of the whole figure, find the area of the piece, and subtract.

Other Perimeters

For any perimeter, just add the outside lengths all the way around.

Practice

1. Find the area of a circle with a diameter of 6.
1. 36π
2. 24π
3. 16π
2. What is the area of the triangle above?
1. 48
2. 9
3. 12
4. 18
5. 24
3. A box measured 5" wide, long, and 4" high. How many one-inch cube candies could fit in the box?
1. 10
2. 60
3. 90
4. 120
5. 150

1. d. If the diameter is 6, the radius is 3. A = π(3)2= 9π.
2. c. 8 is the base, b, and 3 is the height, h. × 8 × 3 = 12.
3. d. Since foot = 6 inches: 6 × 4 × 5 = 120 cubic inches. The candies measure 1 cubic inch each, so 120 of them will in the box.