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# ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = 1/4 ar (ABC). Is the given statement true or false and justify your answer.

**Solution:**

It is given that

∆ ABC and ∆ BDE are two equilateral triangles

Area (∆ ABC) = √3/4 × (side)²

In an equilateral triangle ABC, AB = BC = AC

= √3/4 × (BC)² …. (1)

D is the mid point of BC

BD = DC = 1/2 BC … (2)

Area of ∆ BDE = √3/4 × (side)²

In an equilateral triangle ∆ BDE, BD = DE = BE

= √3/4 × (BD)²

= √3/4 × (1/2 BC)²

= √3/4 × 1/4 BC²

= 1/4 [√3/4 BC²]

Area of ∆ BDE = 1/4 Area of ∆ ABC

Therefore, the statement is true.

**✦ Try This: **PQRS is a parallelogram whose area is 140 cm² and A is any point on the diagonal QS. Find the area of ∆ ASR.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 9

**NCERT Exemplar Class 9 Maths Exercise 9.2 Problem 4**

## ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = 1/4 ar (ABC). Is the given statement true or false and justify your answer.

**Summary:**

The statement “ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = 1/4 ar (ABC)” is true

**☛ Related Questions:**

- In Fig. 9.8, ABCD and EFGD are two parallelograms and G is the mid-point of CD. Then ar (DPC) = 1/2 . . . .
- PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig. 9.9). Find the area of . . . .
- ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ (Fig. 9.10). If AQ interse . . . .

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