NCERT Class 10 Maths — Chapter 6

Exercise 6.4: Area of Similar Triangles

The ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Use this to find missing areas and sides.

ratio of areasratio of sides squaredarea theorem

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Extra Practice Questions

These questions cover the same concepts as Exercise 6.4. Try solving them to build confidence before or after the textbook exercise.

Ravi was given a triangle with sides 7 cm, 24 cm, and 25 cm. He concluded that it is a right-angled triangle. Which theorem did he most likely use to reach this conclusion?

A.Basic Proportionality Theorem

B.Angle Sum Property of a Triangle

C.Converse of Pythagoras Theorem

D.Midpoint Theorem

Which of the following statements is TRUE regarding similar figures?

A.A. All congruent figures are similar.

B.B. All similar figures are congruent.

C.C. Similar figures always have the same size.

D.D. Similar figures must have corresponding sides equal.

In ΔABC, D and E are points on AB and AC respectively. If AD = 3 cm, DB = 5 cm, AE = 4.5 cm, and EC = 7.5 cm, and ∠A = 60°, what is the measure of ∠AED?

A.50°

B.60°

C.70°

D.80°

For two triangles ΔLMN and ΔRST to be similar by the SAS (Side-Angle-Side) criterion, which of the following sets of conditions is sufficient?

A.LM/RS = MN/ST and ∠M = ∠S

B.LM/RS = MN/ST and ∠L = ∠R

C.LM/RS = LN/RT and ∠M = ∠S

D.LM/RS = MN/ST and ∠N = ∠T

If ΔPQR ~ ΔXYZ and the perimeter of ΔPQR is 60 cm, while the perimeter of ΔXYZ is 45 cm. If PQ = 12 cm, find the length of XY.

A.10 cm

B.9 cm

C.8 cm

D.11 cm

The areas of two similar triangles are 81 cm² and 49 cm². If the altitude of the larger triangle is 4.5 cm, what is the corresponding altitude of the smaller triangle?

A.3.5 cm

B.3.0 cm

C.2.5 cm

D.2.0 cm

A pole of height 10 m casts a shadow of 8 m. At the same time, an apartment building casts a shadow of 20 m. If the building has a flag pole of 2 m on its roof, what is the total height from the ground to the top of the flag?

A.25 m

B.27 m

C.29 m

D.31 m

In ΔABC, D is a point on AB and E is a point on AC such that DE || BC. If AD = 4 cm and DB = 6 cm, and the area of quadrilateral BDEC is 48 cm², what is the area of triangle ADE?

A.64/7 cm²

B.16 cm²

C.24 cm²

D.32 cm²

Two figures are said to be similar if they have the same shape but not necessarily the same size. Which of the following pairs of figures are ALWAYS similar?

A.Two rectangles.

B.Two triangles.

C.Two squares.

D.Two quadrilaterals.

Consider two triangles, ΔABC and ΔXYZ. If AB/XY = BC/YZ = CA/ZX, which similarity criterion applies?

A.AA Similarity

B.SAS Similarity

C.SSS Similarity

D.RHS Similarity

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