Practice with Perimeter and Circumference Topic Index | Algebra Index | Regents Exam Prep Center

Answer the following questions dealing with
perimeter and circumference.  A calculator is needed.

 1. The pied piper and his friends are walking around a track that is shaped like a regular pentagon.   Each side measures 85 feet.  If they make 3 complete trips around the track, how far will they have walked? Choose: 255 ft 500 ft 1275 ft 1530 ft Explanation A regular pentagon has 5 = sides. One trip:  (5)(85)=425 Three trips:  3(425)=1275

 2. Find the perimeter of this rectangle. Choose: 30 34  47 60 Explanation Use Pythagorean Theorem to get height. Opposite sides of rectangle are equal. Perimeter = 5+12+5+12.

 3. The perimeter of this isosceles trapezoid is 92.   Find the value of x. Choose: 10.7 20 26.7 40 Explanation Isosceles means that BOTH legs are x. Perimeter = x + x+2 + x + x+10. 92=4x + 12 80 = 4x 20 = x

 4. Find the perimeter of this trapezoid. Choose: 56 ft. 63 ft. 73 ft. 280 ft. Explanation Perimeter is the distance around the outside. Do not include the 10 in your total.

 5. The diameter of this circular placemat is 15 inches.  Find the circumference to the nearest tenth of an inch. Choose: 22.5 in. 47.1 in. 94.2 in. 176.6 in. Explanation Circumference equals pi times diameter.

 6. Skeeter, the wonder dog, jumps through circular rings as part of his dog show exhibition.  Skeeter requires a width of 18 inches for his costume to clear the ring.  Will a ring with an inner circumference of 39.8 inches be large enough for Skeeter's act? Choose: yes no Explanation Circumference = pi times diameter. 39.8=3.141592654(diameter) diameter=12.66873347 There will not be enough room for Skeeter to jump through.

 7. A large pizza has a circumference of 72.5 inches.  Which of the perimeters listed could belong to the smallest box capable of holding a large pizza? Choose: 23 24 73 96 Explanation Determine the diameter of the pizza. 72.5=3.141592654(diameter) diameter=23.07746675 Diameter of the pizza will equal the length of the side of the box. A perimeter of 96 has a box length of 24.

 8. Find the width of a rectangular vegetable garden if its perimeter is 16.4 m and its length is 5.05 m. Choose: 3.15 m 5.05 m 6.3 m 10.1 m Explanation P = 2(length) + 2(width) 16.4 = 2(5.05) + 2w 16.4 = 10.1 + 2w 6.3 = 2w 3.15 = w

 9. A rectangular football field has side lines 120 yards long.  Each of the end lines is 160 feet long.  What is the perimeter of the football field? Choose: 280 ft 346 ft 880 ft 1040 ft Explanation Beware: this problem has BOTH yards and feet. 120 yards = 360 feet. P=2(length) + 2(width) P=2(360) + 2(160) = 1040

 10. "The perimeter of this rectangle is 46 feet.  I need to get from point A to point B, fast!  What is the shortest distance from A to B?" Choose: 8 ft 15 ft 16 ft 17 ft Explanation Perimeter = 2(length) + 2(width) 46=2(15) + 2w 46=30 + 2w 16=2w w=8 Use Pythagorean Thm to find diagonal or hypotenuse AB.

 11. The side of a regular hexagon measures 12.5 feet.  What is the perimeter of the hexagon? Choose: 62.5 ft 75 ft 125 ft 130.5 ft Explanation Regular means all of the sides are the same length. A hexagon has 6 sides. P = distance around the outside. 12.5 x 6 = 75

 12. In this triangle, AB = 8 and AC = 10.  If the perimeter  of this triangle is three times AB, find BC. Choose: 6 8 10 24 Explanation 3 x AB = 24 = perimeter 8 + 10 + BC = 24 18 + BC = 24 BC = 6

 13. Find the perimeter. Choose: 34 cm 34 sq. cm 56 cm 56 sq. cm Explanation Notice the hash marks showing equal sides. The unlabeled vertical side is 6 cm. Add ALL of the sides. Label in cm.

 14. Find the perimeter. Choose: 68 cm 76 sq. cm 96 cm 101 cm Explanation Use the Pythagorean Theorem to find the hypotenuse of the triangle, which is 20. Add ALL sides.

 15. Serena's garden is a rectangle joined with a semicircle, as shown in the diagram.  Line segment AB is the diameter of semicircle P.  Serena wants to put a fence around her garden.  Calculate the length of fence Serena needs to the nearest tenth of a foot. Choose: 93.4 61.7 42.8 33.4 Explanation Fencing is a perimeter concept. Be sure to use half of the circumference formula. Use radius of 3. Fencing = 9 + 6 + 9 + 0.5(2•pi•3) = 33.4

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