#### Chapter 12 Heron's Formula R.D. Sharma Solutions for Class 9th Exercise 12.2

**Exercise 12.2**

Q1. Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

**Solution**

The quadrilateral ABCD having sides AB, BC, CD, DA and diagonal AC = 5 cm is given, where AC divides quadrilateral ABCD into two triangles Î”ABC and Î”ADC. We will find the area of the two triangles separately and them to find the area of quadrilateral ABCD.

2. The sides of a quadrangular field, taken in order are 26 m, 27 m, 7 m are 24 m respectively. The angle contained by the last two sides is a right angle. Find its area.

**Solution**

We assume quadrilateral ABCD be the quadrangular field having sides AB, BC, CD, DA and ∠CDA = 90°.

We take a diagonal AC, where AC divides quadrilateral ABCD into two triangles Î”ABC and Î”ADC We will find the area of two triangles Î”ABC and Î”ADC separately and add them to find the area of the quadrangular ABCD.

3. The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.

**Solution**

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and angle ∠ABC = 90°.

We take a diagonal AC, where AC divides quadrilateral ABCD into two triangles Î”ABC and Î”ADC. We will find the area of these two triangles and add them to find the area of the quadrilateral ABCD

4. A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9 m, BC = 12 m, CD= 5 m and AD = 8 m. How much area does it occupy?

**Solution**

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and ∠DCB = 90°.

We take a diagonal DB, where DB divides ABCD into two triangles Î”BCD and Î”AB

5. Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.

**Solution**

We assume ABCD be the given trapezium where AB is parallel to DC.

We draw CE parallel to AD from point C.

Therefore, a parallelogram ADCE is formed having AD parallel to CE and DC parallel to AE.

AE = 60 cm; CE = 25 cm; BE = AB-AE = 17 cm

Basically we will find the area of the triangle BCE and area of the parallelogram AECD and add them to find the area of the trapezium ABCD.

6. Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.

**Solution**

We assume ABCD be the given rhombus having

AB = BC = CD = DA

Diagonal DB divides rhombus into two equal triangles BDC and ADB

7. A rhombus, sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m

^{2}. Find the cost of painting.

**Solution**

We assume ABCD be the given rhombus having

AB = BC = CD = DA

BD and AC be the diagonals of rhombus

8. Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm.

**Solution**

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA, diagonal BD and ∠BAD = 90° where BCD forms an equilateral triangle having equal sides.

9. Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.

**Solution**

The quadrilateral ABCD having sides AB,BC,CD,DA and diagonal BD is given, where BD divides ABCD into two triangles

Î”DBC and Î”DAB

10. Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ACB = 90° and AC = 15 cm.

**Solution**

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and ∠ACB = 90

^{∘}.

We take a diagonal AC, where AC divides ABCD into two triangles Î”ACB and Î”ADC

11. The adjacent sides of a parallelogram

*ABCD*measure 34 cm and 20 cm, and the diagonal

*AC*measures 42 cm. Find the area of the parallelogram.

**Solution**

We are given the measure of adjacent sides of a parallelogram AB and BC that is the sides having same point of origin and the diagonal AC which divides parallelogram ABCD into two congruent triangles ABC and ADC.

12. Find the area of the blades of the magnetic compass shown in Fig. 12.27 (Take √11 = 3.32).

**Solution**