Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Similar Polygons

Q1:

𝐴 𝐡 𝐢 𝐷 is a parallelogram with 𝐴 𝐡 = 9 and 𝐡 𝐢 = 5 . Let 𝑋 be a point on ray  𝐴 𝐡 but not on the segment 𝐴 𝐡 , with 𝐡 𝑋 = 1 8 . Let π‘Œ be a point on ray οƒͺ 𝐢 𝐡 but not on the segment 𝐢 𝐡 , with 𝐡 π‘Œ = 1 0 . Let 𝑍 be a point so that 𝑋 𝐡 π‘Œ 𝑍 is a parallelogram. If the area of 𝐴 𝐡 𝐢 𝐷 is 39, what is the area of 𝑋 𝐡 π‘Œ 𝑍 ?

  • A9.75
  • B78
  • C19.5
  • D156
  • E180

Q2:

Given the graph, determine the area of similar polygon 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² in which 𝐡 β€² 𝐢 β€² = 6 .

Q3:

Two similar polygons have areas of 20 in2 and 80 in2. Find the scale factor of the first polygon to the second.

  • A 2 ∢ 1
  • B 1 ∢ 4
  • C 4 ∢ 1
  • D 1 ∢ 2
  • E 1 ∢ 5

Q4:

Two corresponding sides of two similar polygons have lengths of 54 and 57 centimeters. Given that the area of the smaller polygon is 324 cm2, determine the area of the bigger polygon.

Q5:

Two corresponding sides of two similar polygons have lengths of 44 and 76 centimeters. Given that the area of the smaller polygon is 121 cm2, determine the area of the bigger polygon.

Q6:

Given the following figure, find the area of a similar polygon 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² in which 𝐴 β€² 𝐡 β€² = 6 .

Q7:

Given the following figure, find the area of a similar polygon 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² in which 𝐴 β€² 𝐡 β€² = 9 .

Q8:

Given the following figure, find the area of a similar polygon 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² in which 𝐴 β€² 𝐡 β€² = 6 .

Q9:

Given the following figure, find the area of a similar polygon 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² in which 𝐴 β€² 𝐡 β€² = 3 .

Q10:

Given the following figure, find the area of a similar polygon 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² in which 𝐴 β€² 𝐡 β€² = 2 .

Q11:

Given that 𝐴 𝐷 𝐷 𝐢 = 3 2 and the area of β–³ 𝐴 𝐡 𝐢 = 6 9 5 c m 2 , find the area of trapezium 𝐷 𝐢 𝐡 𝐸 .

Q12:

If β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝑋 π‘Œ 𝑍 and 𝐴 𝐡 = 9 5 𝑋 π‘Œ , find a r e a o f a r e a o f 𝑋 π‘Œ 𝑍 𝐴 𝐡 𝐢 .

  • A 1 8 5
  • B 9 5
  • C 3 6 5
  • D 2 5 8 1

Q13:

𝐴 𝐡 𝐢 𝐷 is a square where 𝐴 𝐡 , 𝐡 𝐢 , 𝐢 𝐷 , and 𝐷 𝐴 are divided by the points 𝑋 , π‘Œ , 𝑍 , and 𝐿 , respectively, by the ratio of 4 ∢ 1 . Find the ratio of the area of 𝑋 π‘Œ 𝑍 𝐿 to that of 𝐴 𝐡 𝐢 𝐷 .

  • A 4 8 9 ∢ 5 9 3
  • B 2 5 ∢ 1 7
  • C 5 9 3 ∢ 4 8 9
  • D 1 7 ∢ 2 5
  • E 3 ∢ 5

Q14:

In the given figure, 𝐻 𝐴 𝐷 is an equilateral triangle with a perimeter of 45 cm. Given that 𝐴 𝐷 ∢ 𝐴 𝐡 = 3 ∢ 7 , determine the area of rectangle 𝐴 𝐡 𝐢 𝐷 .

Q15:

Using the figure below, find the ratio between the area of the parallelogram 𝑋 π‘Œ 𝑍 𝐿 and the area of the triangle 𝐴 𝐡 𝐢 in its simplest form.

  • A 2 ∢ 1
  • B 2 2 ∢ 1 5
  • C 5 ∢ 3
  • D 1 2 ∢ 5
  • E 5 ∢ 6

Q16:

Rectangle 𝑄 𝑅 𝑆 𝑇 is similar to rectangle 𝐽 𝐾 𝐿 𝑀 with their sides having a ratio of 8 ∢ 9 . If the dimensions of each rectangle are doubled, find the ratio of the areas of the larger rectangles.

  • A 3 2 ∢ 8 1
  • B 1 2 8 ∢ 8 1
  • C 1 6 ∢ 9
  • D 6 4 ∢ 8 1
  • E 4 ∢ 9

Q17:

Rectangle 𝑄 𝑅 𝑆 𝑇 is similar to rectangle 𝐽 𝐾 𝐿 𝑀 with their sides having a ratio of 5 ∢ 3 . If the dimensions of each rectangle are tripled, find the ratio of the areas of the larger rectangles.

  • A 2 5 ∢ 2 7
  • B 2 5 ∢ 3
  • C 5 ∢ 1
  • D 2 5 ∢ 9
  • E 5 ∢ 9

Q18:

Rectangle 𝑄 𝑅 𝑆 𝑇 is similar to rectangle 𝐽 𝐾 𝐿 𝑀 with their sides having a ratio of 9 ∢ 5 . If the dimensions of each rectangle are tripled, find the ratio of the areas of the larger rectangles.

  • A 2 7 ∢ 2 5
  • B 2 4 3 ∢ 2 5
  • C 2 7 ∢ 5
  • D 8 1 ∢ 2 5
  • E 3 ∢ 5

Q19:

Rectangle 𝑄 𝑅 𝑆 𝑇 is similar to rectangle 𝐽 𝐾 𝐿 𝑀 with their sides having a ratio of 4 ∢ 7 . If the dimensions of each rectangle are doubled, find the ratio of the areas of the larger rectangles.

  • A 8 ∢ 4 9
  • B 3 2 ∢ 4 9
  • C 8 ∢ 7
  • D 1 6 ∢ 4 9
  • E 2 ∢ 7

Q20:

Triangle is right at , where and . Suppose , , and are similar polygons on corresponding sides , , and . If the area of is 145, what are the areas of and to the nearest hundredth?

  • A area of , area of
  • B area of , area of
  • C area of , area of
  • D area of , area of

Q21:

Given the figure shown, determine the area of a similar polygon, 𝐴 β€² 𝐡 β€² 𝐢 β€² , in which 𝐴 β€² 𝐡 β€² = 3 .

Q22:

Given the figure shown, determine the area of a similar polygon, 𝐴 β€² 𝐡 β€² 𝐢 β€² , in which 𝐴 β€² 𝐡 β€² = 6 .