Practice with Area of Polygons and Circles Topic Index | Algebra Index | Regents Exam Prep Center

Answer the following questions dealing with area of polygons and circles.  Grab your calculator.

 1. Find the area. Choose:  32.5 sq. units 400 sq. units 500 sq. units 600 sq. units Explanation Area = (1/2) base times height The base is 40. The height is 25.

 2. Find the area of the green rectangle. Choose:  30 sq. units 60 sq. units 144 sq. units 156 sq. units Explanation Area = base times height The base is 12. Use Pythagorean Theorem to get height. The height is 5.

 3. Jessica is making a circular table cloth for an art project.  She wants half of the cloth to be a plain colored fabric and half to be a print fabric.  How many square yards of each fabric (to the nearest hundredth of a yard) will she actually be using if the diameter of the cloth is 6 feet? Choose:  1.57 sq. yds 1.58 sq. yds 14.13 sq. yds 14.14 sq. yds Explanation Diameter 6 feet = radius 3 feet or 1 yard. Each fabric is a semi-circle. Area of semi-circle = one-half area of circle. A = (0.5)( pi)(1)²

 4. Lin is planting a circular garden of tulips.  She plans to plant four different colors in equal amounts.  The garden will have a diameter of 24 feet.  How many square feet, to the nearest foot, of space will she have for each of the colors? Choose:  9 sq. ft. 113 sq. ft.  226 sq. ft. 452 sq. ft. Explanation The radius of the garden is 12 feet. Each color will have 1/4 of the total area. Area for color = 0.25 (pi) 12²

 5. Find the area of this trapezoid. Choose: 63 sq. units 180 sq. units 360 sq. units 1120 sq. units Explanation Area=one-half the height times the sum of the bases The height is 10. The bases are 8 and 28.

 6. The diagram at the left shows a green piece of square carpeting.  A hole is being cut out of the carpeting for a column 6' in diameter.  How many square feet of carpeting are shown in this diagram?  Round answer to the nearest tenth of a square foot. Choose: 108.0 sq.ft. 211.0 sq.ft. 295.7 sq.ft. 324.6 sq.ft. Explanation Area of square = 324. The radius of the circle is 3. Area of circle = 28.27433388. Subtract the area of the circle from the area of the square.

 7. A yield sign has the dimensions given in the diagram.  How many square inches of material are needed to make the sign?  Round answer to the nearest tenth of a square inch. Choose: 108.0 sq.in. 324.6 sq.in. 561.2 sq.in. 648.0 sq.in. Explanation Use the special formula for equilateral triangles, or cut the triangle in half, use Pyth.Thm. to find the height and then find the area.

 8. The area of a trapezoid is 28 sq. ft.  The bases are 5 ft. and 9 ft.  What is the height of the trapezoid in feet? Choose: 4 ft. 5 ft. 6 ft. 9 ft. Explanation Area=1/2(h)(b1+b2) 28=1/2(x)(5+9) 28=1/2(x)(14) 28=7x x=4

 9. The school band is selling pennants.  Each pennant is cut in the shape of a triangle 4 feet long and 1 foot high.  How many square feet of fabric are needed to make 200 pennants (assuming no waste)? Choose: 100 sq.ft 200 sq.ft 400 sq.ft 800 sq.ft Explanation The area of the triangle is 2 square feet. Remember the formula Area = one half base times height. To make 200 pennants you need 200 times 2 sq. ft.

 10. Find the area of parallelogram ABCD. Choose: 504 sq. units 672 sq. units 768 sq. units 822 sq. units Explanation Area=base times height. The base is 21. The height is 24.

 11. Tom plans to make a strawberry shortcake to take to a party.  The recipe calls for a 10 inch diameter round pan.  Tom only has an 8 inch square pan, a 9 inch square pan and a 10 inch square pan.  Which pan comes closest in area to the one that the recipe suggests? Choose: 8 inch pan 9 inch pan 10 inch pan Explanation Remember to use 5 as the radius for the round pan. The round pan has an area of 78.5 sq. in. The area of the 8 inch square pan is 64 sq. in.. The area of the 9 inch square pan is 81 sq. in. The area of the 10 inch square pan is 100 sq. in.

 12. A 20 ft. by 15 ft. swimming pool is surrounded by a 2 ft. wide sidewalk.  A fence on the edge of the sidewalk encloses the whole pool area. a.  What is the area in square feet inside the fence? b.  What is the area in square feet of only the sidewalk? Choose: a. 300 sq.ft. 374 sq.ft. 456 sq.ft. b. 156 sq.ft. 300 sq.ft. 374 sq.ft. Explanation Dimensions of the entire pool area are 24 ft. by 19 ft. The area inside the fence is 24 times 19. The area of the sidewalk is the total area from part a subtract the area of the pool (20 by 15 or 300 sq.ft.)

 13. (optional question) Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to the nearest tenth of a square unit. Choose: 0.3 sq.units 15.7 sq.units 19.7 sq.units 50.3 sq.units Explanation Determine the fractional part of the area needed. Form a fraction of the arc length to the total circumference. Area of sector = 7.85/(2•pi•r) • area of circle

 14. Butch, the dog, is leashed to the corner of the house when he is outdoors alone.  The leash is 20 feet long.  Find the amount of ground area available to Butch when leashed outdoors.  (Assume the corner of the house to be a right angle and the dimensions of the house to exceed 20 feet..) Choose: 251.3 sq.ft. 314.2 sq.ft. 628.3 sq.ft. 942.5 sq.ft. Explanation Since the corner of the house is a right angle, one-fourth (90/360) of Butch's circle is blocked by the house. Three fourths of the area is available to Butch. 0.75 • pi • r²

 15. Find the number of square inches in the area of the shaded region of this square which is being intersected by two semicircles.  Leave answer in terms of . Choose: sq.in sq.in sq.in   sq.in Explanation Find the area of the square. 11 x 11 = 121 sq.in. Find the area of the circle. PI * 5.5². Subtract.

 16. Find the area of this figure. Express the answer to the nearest tenth of a square inch. Choose: 356.5 sq.in 457.1 sq.in 658.1 sq.in 1060.2 sq.in Explanation Find the area of the square. 16 x 16 = 256 sq.in. Find the area of the semicircle. (1/2)* PI * 8². Add.

 17. Find the area of this figure. Express the answer to the nearest tenth of a square cm. Choose: 56.5 sq.cm 140.5 sq.cm 310.2 sq.cm 478.2 sq.cm Explanation Find the area of the triangle. (1/2) x 14 x 12 = 84 Find the area of the semicircle. (1/2)* PI * 6². Add.

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