WP6a
Practice - Perimeters and Areas
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. A rug has an area of 64 square feet and a perimeter of 40 square feet. What are the dimensions of the rug?
2. A pipe has an outer diameter of 6 inches and an inner diameter of 5 inches How thick is the pipe?
3. Your rectangular garden has an area of 324 square feet. You want to fence it in. The shorter side is 12 feet. How much fence should you buy?
4. The area of a parallelogram is 8b, where b is the length of the base. The area of a right triangle is 8d, where d is the length of a shorter side. What is the ratio of the area of the parallelogram to the area of the triangle?
5. What is the area of a parallelogram with base b = 8, height = 3.7, and with one side = 4.3?
6. The area of a rectangle equals its length times its width. If you multiply the length by three but keep the width the same, by what percentage is the rectangle's area increased?
7. A right triangle has one short side equal to 4 and the second short side equal to 2-1/2. What is the area?
8. A circular pond has a concrete wall around the edge. The diameter of the pond is 10 feet. What is the area of the pond? What is the length of the wall around the pond?
9. If the area of a circle is 36π , what is the diameter?
ANSWERS
1. x times y = 64. 2x plus 2y = 40. y = 64/x. 2x plus 2(62/x) = 40.
2. 1/2 inch. The formulas are not relevant.
3. 12 times x = 324. x = 324/12 = 27. Perimeter = (2 x 12) + (2 x 27) = 24 + 54 = 78 feet.
4. The area of a parallelogram is the height h times the base b, or A(p) = hb. The area of a right triangles is ½ of one short side times the other short side, A(t) = ½ ab. Then A(p)/A(t) - hb/(½ab) = 8h/4b. The parallelogram has twice the area of the right triangle.
5. From the formula sheet built into the test, you can see that the area equals the base times the height. The length of the side is not relevant. So the area is 8 x 3.7 = 29.6.
6. A = L x W. The ratio of the area of the larger rectangle to the area of the smaller rectangle is (3LW / LW) = 3. The increase is from 1 to 3. The percentage increase is 2/1 = 200%.
7. The area of a right triangle is (L x W)/2 = (4 x 2 ½ )/2 = 2 x 2½ = 5.
8. The area is πr², where r = d/2 = 5. So A = π 5 ² = 25 π . The circumference is π d = 10 π .
9. A = π r ² = 36π , so r = 36 and r = 6.