AREA OF SIMILAR SOLIDS WORKSHEET
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Consider the following similar shapes. Find
i) the scale factor
ii) the length or area marked by the unknown.
Problem 1 :
Problem 2 :
Problem 3 :
Problem 4 :
Problem 5 :
Problem 6 :
Problem 7 :
Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter and area of the smaller triangle.
Problem 8 :
You are making a scale model of a rectangular park for a school project. Your model has a length of 2 feet and a width of 1.4 feet. The actual park is 800 yards long. What are the perimeter and area of the actual park?
Problem 9 :
Figure A has an area of 48 square feet and one of the side lengths is 6 feet. Figure B has an area of 75 square feet. When the figures are similar, find the missing corresponding side length.
Problem 10 :
Figure A has an area of 18 square feet. Figure B has an area of 98 square feet and one of the side lengths is 14 feet. When the figures are similar, find the missing corresponding side length.
Problem 11 :
In the following exercises, JKLM ∼ EFGH.
a) Find the scale factor of JKLM to EFGH.
b) Find the scale factor of EFGH to JKLM.
c) Find the values of x, y, and z.
Answer Key
1) i) k = 1/2 ii) 5 cm
2) i) k = 3/2 ii) 18 cm2
3) i) k = 5/2 ii) x = 4 cm2
4) i) k ≈ 0.548 ii) 4.38 cm
5) i) k ≈ 0.758 ii) ≈ 3.18 m
6) k ≈ 1.45 ii) x = 33.29 cm2
7) the perimeter of the smaller triangle is 32 meter.
the area of the smaller rectangle is 120 square meters.
8) Area of rectangular park = 448000 square feet
Perimeter of actual park = 2720 feet
9) Missing side is x = 7.5 feet
10) the missing side is 6 feet.
11) a) 5 : 2
b) 2 : 5
c) x = 27.5, y = 12 and z = 65
The two polygons are similar. Find the value of x.
Problem 1 :
Problem 2 :
Problem 3 :
Problem 4 :
Problem 5 :
Problem 6 :
Problem 7 :
Problem 8 :
Problem 9 :
Problem 10 :
Figure A has a perimeter of 60 inches and one of the side lengths is 5 inches. Figure B has a perimeter of 84 inches. Find the missing corresponding side length.
Problem 11 :
Figure A has an area of 4928 square feet and one of the side lengths is 88 feet. Figure B has an area of 77 square feet. Find the missing corresponding side length.
Problem 12 :
In the diagram triangle ABC ~ triangle ADE
a) Find the scale factor from triangle ABC to ADE
b) Find the value of x
c) Find <ABC
d) The perimeter of triangle ABC is about 42.4 units. Find the perimeter of triangle ADE.
e) The area of triangle ABC is about 71.75 square units. Find the area of triangle ADE
f) Is BC || DE explain your reasoning.
Problem 13 :
ABCDE ~ KLMNP
a) Find the scale factor from ABCDE to KLMNP.
b) Find the scale factor from KLMNP to ABCDE.
c) Find the values of x, y, and z.
d) Find the perimeter of each polygon.
e) Find the ratio of the perimeters of ABCDE to KLMNP.
f) Find the ratio of the areas of ABCDE to KLMNP.
Answer Key
1) x = 43
2) x = 11.5
3) x = 2.27
4) x = 14
5) x = 6
6) x = 40
7) x = 7.5
8) x = 7
9) x = 6
10) the missing side is 7 inch.
11) the measure of missing side is 616 feet.
12) a) 4 : 7
b) x = 7.5
c) ∠ABC = 108
d) Perimeter of triangle ADE = 74.2
e) Area of triangle ADE = 219.73 square units.
f) Since corresponding sides are equal, the sides BC and DE are parallel.
13)
a) The scale factor from ABCDE to KLMNP = 2 : 3
b) The scale factor from KLMNP to ABCDE = 3 : 2
c) x = 3/2, y = 4.5√2 and z = 45
d) Perimeter of polygon ABCDE = 6 + 3√2
Perimeter of polygon KLMNP = 9 + 4.5√2
e) Since the corresponding sides is in the ratio 2 : 3, then the perimeter will also be in the same ratio.
f) Area of ABCDE = 3.5 square units
Area of KLMNP = 6.75 square units
Related Pages
- Finding unknown in similar solids
- Determine if the shapes shown are similar congruent or neither
- Find the missing side of similar figures
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