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Exploring the Perimeters of Various Geometric Shapes

This guide delves into the perimeter calculations for a variety of geometric shapes, including rectangles, squares, hexagons, and polygons. Examples range from finding the perimeter of a rectangular plot of land to determining the side lengths of a regular heptagon and an octagon. The exercises encourage application of perimeter formulas and offer insights into the relationships between different dimensions, showcasing how increasing size affects calculations. Useful for students and enthusiasts of geometry, this resource provides practical applications for real-world scenarios.

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Exploring the Perimeters of Various Geometric Shapes

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  1. #6) The perimeter of a rectangular piece of land 3 miles long and  mile wide is 8 miles. #7) The perimeter of an equilateral hexagon with one side of length 14 mm is 84 mm. #8) The perimeter of a square with side tis 4t. #9) The perimeter of a regular heptagon with side (x + 1) is 7x + 7. #10) The perimeter of a rectangle is 70, one side is 3 times the length of the others. The sides are8.75 & 26.25 units long. #11) A poster is 1.5 times as wide as it is high and its perimeter is 3 m The poster is 0.9 m long and 0.6 m wide . Assignment #1: pp.438-440

  2. #12) The perimeter of a rhombus is 2 feet. a. This is enough information to find the length of each side. b. Each side is  ft long. #13) A stop sign is a regular octagon. If its perimeter is 10’, one side has a length of 1.25 ft. #14) The perimeter of an equilateral triangle is p, one side has length p units long. m #15) The boundary of the museum on p.435 is given a. P = 8s + 18m + 2l b. If s = 25, m = 50, l = 100 P = 1300 m s l #16) When the dimensions of a rectangle are multiplied by 5, its perimeter is also multiplied by 5. Assignment #1: pp.438-440

  3. #17) A rectangle with perimeter 16 can have: a. length x 1 2 3 4 5 6 7 width y 7 6 5 4 3 2 1 b. y = -x +8 c. length =  width = 7 #18) One side of an equiangular pentagon has measure 7” but you cannot determine the perimeter. Equiangular means equal angles not equal sides. #19) The measure of each angle in a regular n-gon is #20) mBDC = 131 C 139 A D B Assignment #1: pp.438-440

  4. #1) Rectangle ABCD has dimensions 8.3 cm and 11.4 cm a. Use square centimeters for area. b. Area(ABCD) = 94.62sq cm 5 A B #2) a. Area(ABFG) = 35 sq units b. Area(CDEF) = 16 sq units c. Area(ABCDEG) = 15 sq units 4 C 7 D 4 G E F #3) We use the additive property to solve part c above. #4) a. Area = 315 sq units b. #8) There are 9 sq ft in a sq yd. #9) a. Area = 100 b. Area = a2 (7,20) (20,20) (0,10) (10,10) (7,15) (0,15) (0,a) (a,a) (20,10) (15,10) (15,0) (a,0) (10,0) Assignment #2: pp.445-446

  5. #10) Area(BCDNEM) = 192 sq units #13) a. 24” by 12” = 288 sq in b. 2’ by 1’ = 2 sq ft c. There are 144 sq in a sq ft D C N E 16 #14) The sides of a square are tripled a. The perimeter is tripled. b. The area is multiplied by nine. A M B #11) Area of a rectangle = 50 sq yd, Length = 100 yd, Width = yd #15) Area of a 100 yd by 60 yd field is 300 ft by 180 ft is 54000 sq ft. Area of a 1.5 ft by 6 ft piece of sod is 9 sq ft. So you’ll need 6000 rolls. #12) a. A = 49 sq un, s = 7 un b. A =  sq un, s  1 un c. A = 200 sq un, s  14 un d. A = 3141 sq un, s  56 un Assignment #2: pp.445-446

  6. #16) Perimeter of a regular pentagon = 13. Length = 2.6 #17) Perimeter of a regular pentagon = 462 cm, length one side= 185 the other length = 46 #18) Length one side of rhombus = 3x Perimeter = 12x 25 m #19) a. Perimeter of fence = 230 m b. If perimeter of fence = 200, the fence is 6.25 m from the pool 10 m 50 m #20) Perimeter of triangle =45 4.5x = 45 the sides are 10, 20 and 15 units long 2x 1x x Assignment #2: pp.445-446

  7. In problems #8, 9, 12 your answer may vary #8a.0.65625 sq in #8b.0.703126 sq in #9. 64 sq km #10a. There are 27,878,400 sq ft in one sq mile #10b. There are 43,560 sq ft in one acre. #11 The lake is 215/640 or about 35% of a sq mile. #12 One half area is 21780 sq ft so the dimension could be 121ft by 180 ft #13 If 1 mile = 1.6 km, 1 sq mile = 2.67 sq km and 20 sq miles = 51.2 sq km so the 20 sq miles is greater then 30 sq km. #14a. If AB = 7, HE = 5, then shaded area = 24 sq units #14b. If AB = x, HE = 5, then shaded area = x2 - 25 sq units Assignment #3: pp.450-452

  8. #15 The sides of a rectangle are multiplied by 10 a. The perimeter is multiplied by 10. b. The area is multiplied by 100. #16 Along the 10 ft or 30 in. side you’ll need four. Along the 12 ft or 36 in. side you’ll need five. So you’ll need 20 tiles. #17 Area of rectangle = 96, width = 4, so the length = 24 units. #18 If the area is in square kilometers, then the natural unit for perimeter is kilometers. In problems #19 & # 6 your answer may vary. p.486 #9a.4800 sq miles #9b.4200 sq miles #9c.3950 sq miles p.458 #8a.284,200 sq miles #8b.270,725 sq miles Assignment #3: pp.450-452; p.458; p.486

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