Math Area of Irregular Figures

Name _______________ Date ____ Class _____ n Problem Solving ii; Area of Parallelograms �sso� Write the correct answer. 1. A dollar bill has an area of 15.86 square inches. If a dollar bill is 2.6 inches long, how wide is it? lo.I inches 3. A back yard is shaped like a parallelogram with a height of 32 feet and a base of 100 feet One bag of grass seed covers 125 square feet What is the least number of bags of seed needed to seed the lawn? ·�lQ \() l l1S ·\. <.":'°'(j 2. On an official United States flag, the ratio of width to length is exactly 1 to 1.9. What is the area of a United States flag whose width is 2 feet? · 7 ' lp .(;{-'3- 4. The art club is painting a mural on a school wall. The mural is in the shape of a parallelogram. If the base of the mural is 10.5 feet long and the mural covers 89.25 square feet, how high is the mural? i.cs ff hie� LI Choose the letter of the correct answer. C) 5. In baseball, the area of each base is 225 square inches. Each base is a square. What is the length of each side of a base on a baseball field? C 25 in. A 12 in. B 22.5 in. �5 in. 6. The area of a parallelogram is 632.1 square centimeters. Its base is 24.5 centimeters. What is the height t he parallelogram? ,� '{ H 21.9 cm V5,8 cm J 11.8 cm G 705.6 cm 7. The official rules for volleyball were developed in 1897. The rules state that the court or floor space must be 25 feet wide and 50 feet long. An official basketball court is 94 feet by 50 feet. How much larger is the area of a basketball court than the area of a volleyball court? A 69 fl2 larger @),450 ft2 larger C 1 ,250 ft2 larger D 4,700 ft2 larger 8. Two parallelograms each have an area of 288 square inches. One has a height of 12 inches, and the other has a height of 18 inches. What are the bases of each parallelogram? F 40 in. and 30 in. G 22 in. and 15 in. @ 4 in. and 16 in. J 26 in. and 20 in. Name _______________ Date ____ Class _____ Gonzalez Builders purchased the four lots shown below. The company intends to build homes on the lots and needs to know the total area in square feet of each lot. They also need to know the perimeter in feet of each lot. You can use proportions to calculate the areas and perimeters. For each figure, the scale is 1 inch: 60 feet. 3 in. 1 in. 1 in. 1.5 in. Lot A [o.5 in. �---' 2 in. 2.5 in. 1.5 in. 0.5 in. 0.75 in. 1. total area 0.75 in. 1 in. 3 in. 0.75 in. 1L�OO f�z. J,-'4....·0_·li·� -- perimeter _(-· 2 in. 2 in. LotC 2.5 in. 1.5 in. �t-0'--;-,�fC �f-;�'" o�"' �C� - r- 'l ,_ per·1meter __Ji�-_._.1 -_-. �,J-l "l - �11_,,,_• -1'0:"'1:f--1 1.75 in. Lot D 0.5 in. 4. total area perimeter 0.5 in. 3 in. ,;? 1 . lJ O O f-{'Z- r, flJ,. l,Q 1.-/ o j_,I ' '. 5. What is the combined area of all four lots? _1�1 .._1 !{;""' :)_t: _;)(_ . '-")-'-u -'-:z. ___ "" '--'6. What length of fencing would be needed to enclose all four lots during construction? 1.75 in. 1 in. 1 in. 1.25 in. 3. total area Lot B 2. total area 1 in. 1.5 in. a, q lfJo -tr I Name -_______________ Date ---- Class ----- Area of Triangles and Trapezoids Write the correct answer. The diagram shows the dimensions of the sails on a model sailboat. Use the diagram to solve Problems 1-2. 1. About how much material to the nearest square foot will be needed to make the sails? . (J\�01.tT i19t ;i::: I{) 1 ft \\Ott Loa,tld need J-1 1.25 ft 1.25 ft ·"Z,,, 2. If the dimensions for each sail were doubled, how would that change the total amount of material needed to make the sails? = ;i::: I{) I , I 1\fi\t.S a\ rf)U,ciJ. 3. A flower bed is shaped like a trapezoid with a height of 3.5 yards, one 2.8-yard base, and another (-) •. 4.6-yard base. A packet of flower seeds covers 5.6 square yards. What is the least number of packets needed to plant the flower bed? 4. A triangular road sign has a height of 8 feet and a base of 16.5 feet. How much larger in area is this sign than one with a height of 4 feet and a base of 8.25 feet? 3 pa.r/l1J( Choose the letter of the correct answer. This diagram shows the top view of the roof of a house. North :5.4 m West 10 m 8.5 m Center 5.5 m East 8m 5 .4m South 5. If you need to reshingle the north and south sections of the roof, how many square meters of shingles will you need? C 49.95 m2 A."' 199.8 m2 �9.9m2 D 459m2 6. If you need to reshingle the west section of the roof, how many square meters of shingles wiU you need? tfik6.45 m2 F 13.5 m2 G 18.9m2 J 72.9m2 lip�; Problem Solving • •Z,C 4rea of Irregular Figures .c:...·· t.. . , , .· ,, \ ( 1/ ·-f I l () W Lu O fL- t Write the correct answer. 1. Explain how to find the area of the irregular figure below. Then find the area. 10ft 2. Mr. Bemis carpets the living room shown below. If he pays $20 per square meter, what is the total cost of the carpet? 10 ft 25 ft 3m 11 m 3. A figure is made of a square and a semi-circle. The square has sides of 16 cm each. One side of the square is also the diameter of the semi-circle. What is the total area of the figure? 4. A figure is made of a rectangle and an isosceles right triangle. The rectangle has sides of 6 in. and 3 in. One of the short sides of the rectangle is also one of the legs of the right triangle. What is the total area of the figure? ·17 r 0L :t/1,rf)., . ) I Choose the letter of the correct answer. 5. Norene builds the deck at the right. The area of the deck is 1 O m2 greater than was originally planned. What is the area of the deck? A110m2 C66m2 D 56 m2 @76 m 2 6. The grid to the right shows a swimming pool. Each square represents 1 square meter. What is the best estimate of the area of the ·1'\ swimming pool? (!ys1 m2 F 45 m2 G 41 m2 J 32 m 2 4m 10 m 2m 10 m I\ ,,. Name _______________ Date ____ Class _____ � li!AP ; Challenge �IC Figure it Out! ;J.-hu UJ Sometimes there is more than one way ' to find the area of an irregular figure. WO ( /.l. 12 m 10m 8m 22m One Way Another Way 12 m 12 m 10m 10 m 20 m 8m 8m 12 m 22m 22m A(rectangle) = 22 • 8 = 176 ft' A(rectangle) = 10 • 8 = 80 ft' A(triangle)= A(trapezoid) ! ·12 • 12 = 72 ft' = ! · 12 • (20 + 8) = 168 ft' A(figure) = 80 + 168 = 248 ft' A(figure) = 176 + 72 = 248 ft' Show two different ways to find the area of each figure. 1. One Way 21 ft Another Way 12 ft 9 ft --2. Area= ·"7 :,�. tr1- Area= 4 • L, GI� rn . , , 6m 11 m 7m 12 m 3. 10ft 16 ft - 4 ft I I 18 ft [v Area= ·7·33 gf'L