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# Calculate the area of the shaded region in Fig. 12.1.

**Solution:**

Given, the figure represents two triangles

We have to find the area of the shaded region.

Consider triangles ABC and BDC

Area of shaded region = area of triangle ABC - area of triangle BDC

By __Heron’s formula__,

Area of triangle = √s(s - a)(s - b)(s - c)

Where s= semiperimeter

s = (a + b + c)/2

In triangle ABC,

a = 120m

b = 122 m

c = 22 m

So, s = (120 + 122 + 22)/2

= 264/2

s = 132 m

Now, area = √[132(132 - 120)(132 - 122)(132 - 22)]

= √[132(12)(10)(110)]

= √[11 × 12 × 12 × 10 × 10 × 11]

= 11 × 12 × 10

Area of triangle ABC = 1320 m²

In triangle BDC,

a = 24 m

b = 26 m

c = 22 m

s = (22 + 24 + 26)/2

= 72/2

s = 36 m

Area = √36(36 - 24)(36 - 26)(36 - 22)

= √36(12)(10)(14)

= √12 × 3 × 12 × 5 × 2 × 7 × 2

= (12 × 2)√5 × 7 × 3

= 24√105

= 24(10.25)

Area of triangle BDC = 246 m²

Area of shaded region = 1320 - 246

= 1074 m²

Therefore, the area of shaded region is 1074 m²

**✦ Try This: **In the given figure AB=16 cm, then find the area of the shaded region

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 12

**NCERT Exemplar Class 9 Maths Exercise 12.3 Sample Problem 2**

## Calculate the area of the shaded region in Fig. 12.1.

**Summary:**

The area of the shaded region in Fig 12.1 is 1074 m²

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