FINDING UNKNOWN IN SIMILAR SOLIDS WORKSHEET

The two polygons are similar. Find the value of x.

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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.

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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.

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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.

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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.

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Find x given that the figures are similar :

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Problem 7 :

A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool

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Problem 8 :

In the diagram, △ABC ∼ △DEF. Find the area of △DEF.

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Problem 9 :

A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.

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Problem 10 :

Describe and correct the error in finding the area of rectangle B. The rectangles are similar.

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Problem 11 :

In the following the two polygons are similar. Find the values of x and y.

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Problem 13 :

In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.problems-on-similar-shapes-q6.png

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Problem 1 :

Lance and Alien is 5 feet tall. His shadow is 8 feet long.

At the same time of day, a tree's shadow is 32 feet long. What is the height of the tree ?

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Problem 2 :

Pentagon JKLMN is similar to pentagon VWXYZ, what is the measurement of angle X ?

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Problem 3 :

Triangle PQR is similar to triangle DEF as shown.

which describes the relationship between the corresponding sides of the two triangles ?

a)  PQ/DE = 4/6        b)  PQ/DE = 6/4

c)  PQ/EF = 4/9        d)  PR/DE = 6/6

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Problem 4 :

A six foot tall person is standing next to flag pole. The person is casting a shadow 1 1/2 feet in length while a flagpole is casting a shadow 5 feet in length. How tall is the flagpole ?

a)  30 ft     b) 25 ft    c)  20 ft     d)  15 ft

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Problem 5 :

The angle of the roof on Kaya's doll house is 56°. She built a scale model of the doll house with a scale ratio of 1 : 4, what is the measure of the angle of the roof of the model ?

a) 14°     b) 34°    c) 56°    d)  224°

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Problem 6 :

In triangle PQR is similar to XYZ.

What is the perimeter of XYZ ?

a) 21 cm     b) 63 cm    c) 105 cm    d)  126 cm

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Problem 7 :

If the triangles ADE and ABC shown in the figure below are similar, what is the value of x ?

a) 4     b) 5    c) 6    d)  8     e)  10

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Problem 8 :

In the figure given below, the two triangles are similar. What is the value of x ?

a) 12.4     b) 13.2    c) 14    d)  18.6     e)  22.1

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Problem 9 :

Mr. Smith is having some photos enlarged for studio. He wants to enlarge a photo that is 5 inches by 7 inches so the dimensions are 3 times larger than the original. How many times larger than the original photo will the area of the new photo be ?

a) 3     b) 6    c) 9    d)  30

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Problem 10 :

During a total eclipse of the Sun, the moon is directly in line with the Sun and blocks the Sun’s rays. The distance DA between Earth and the Sun is 93,000,000 miles, the distance DE between Earth and the moon is 240,000 miles, and the radius AB of the Sun is 432,500 miles. Use the diagram and the given measurements to estimate the radius EC of the moon.

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