# Worksheet: Similar Triangles

Q1:

Given that , , and , find the length of .

Q2:

Find the value of .

• A2
• B
• C
• D

Q3:

These two rectangles are similar. Given that the area of the yellow one is 69.3 cm2, find the area of the green rectangle.

Q4:

If , evaluate .

• A
• B97
• C
• D

Q5:

In the given figure, and are parallel. Use similarity to work out the value of .

• A
• B
• C
• D
• E

Q6:

where and . If the area of , what is the area of ?

Q7:

The diagonal of a small square is of the length of the diagonal of a larger square. If the area of the smaller square is 9 cm2, what is the area of the larger square?

Q8:

Given that and the area of , find the area of .

Q9:

where and . If the area of is 1β848 cm2, what is the area of ?

Q10:

If the ratio between the sides of two similar polygons is , what is the ratio between their areas?

• A
• B
• C
• D
• E

Q11:

Square A is an enlargement of Square B by a scale factor of . If the perimeter of Square A equals 56 cm, what is the area of Square B? Give your answer to the nearest hundredth.

Q12:

It cost to fit wooden flooring in a class with dimensions 28 m and 10 m. How much would it cost to fit wooden flooring in a similar room with dimensions 84 m and 30 m.

Q13:

If , find the scale factor of similarity of to and the values of and .

• A scale factor, ,
• B scale factor, ,
• C scale factor, ,
• D scale factor, ,
• E scale factor, ,

Q14:

Given that the similarity ratio of polygon to polygon and the similarity ratio of polygon to polygon , find the similarity ratio of polygon to polygon .

• A
• B
• C
• D

Q15:

Given that , , , and , find the length of .

Q16:

Triangles and are similar.

Work out the value of .

Work out the value of .

• A
• B
• C7
• D6
• E

Q17:

In the figure, suppose also that , and that . What is the length ?

Q18:

In triangle , let be a point on and a point on . Suppose that and that . If the area of is 237, what is the area of the trapezoid ?

• A131.67
• B94.8
• C85.32
• D151.68
• E211.34

Q19:

Find the value of rounded to the nearest hundredth, if needed.

Q20:

The areas of two similar polygons are in the ratio . What is the ratio between corresponding sides? What is the ratio between their perimeters?

• A ,
• B ,
• C ,
• D ,

Q21:

If , the area of of the area of , and , find the length of .

• A cm
• B 26 cm
• C 6 cm
• D cm

Q22:

Triangles and are similar. Find to the nearest integer.

Q23:

Triangle can be dilated by a scale factor of two onto triangle .

Determine the length of .

Determine the length of .

Find the measure of angle .

Q24:

Given that is a square, , and , find .

• A
• B110
• C15
• D10

Q25:

Triangles and are similar.

Work out the measure of angle .

Work out the value of .

Work out the value of .