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

**Solution:**

We divide the quadrilateral into two triangles, and by using Heron’s formula, we can calculate the area of triangles.

Heron's formula for the area of a triangle is: Area = √[s(s - a)(s - b)(s - c)]

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle

Now, ABCD is quadrilateral shown in the figure

For ∆ABC, consider

AB^{2} + BC^{2} = 3^{2} + 4^{2 }= 25 = 5^{2}

⇒ 5^{2 }= AC^{2}

Since ∆ABC obeys the Pythagoras theorem, we can say ∆ABC is right-angled at B.

Therefore, the area of ΔABC = 1/2 × base × height

= 1/2 × 3 cm × 4 cm = 6 cm^{2}

Area of ΔABC = 6 cm^{2}

Now, In ∆ADC

we have a = 5 cm, b = 4 cm and c = 5 cm

Semi Perimeter: s = Perimeter/2

s = (a + b + c)/2

s = (5 + 4 + 5)/2

s = 14/2

s = 7 cm

By using Heron’s formula,

Area of ΔADC = √[s(s - a)(s - b)(s - c)]

= √[7(7 - 5)(7 - 4)(7 - 5)]

= √[7 × 2 × 3 × 2]

= 2√21 cm^{2}

Area of ΔADC = 9.2 cm^{2} (approx.)

Area of the quadrilateral ABCD = Area of ΔADC + Area of ΔABC

= 9.2 cm^{2} + 6 cm^{2}

= 15.2 cm^{2}

Thus, the area of the quadrilateral ABCD is 15.2 cm^{2}.

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

**Video Solution:**

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

Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.2 Question 2

**Summary:**

We have found that area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm is 15.2 cm^{2}.

**☛ Related Questions:**

- Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.
- A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
- A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
- An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (See Fig. 12.16), each piece measuring 20 cm, 50 cm, and 50 cm. How much cloth of each colour is required for the umbrella?

visual curriculum