This document contains 3 questions and solutions regarding calculating areas of different shapes using Heron's formula. The first question involves calculating the area of a park shaped as a quadrilateral using the lengths of its sides and Pythagoras theorem. The total area is calculated to be 65.4 sqm. The second question calculates the area of another quadrilateral where the lengths of sides are given. The total area is found to be 15.2 sqcm. The third question asks to find the total area of paper used to make a picture of an airplane made of different shapes. The solutions breaks down calculating the individual areas.

1. HERON’S
FORMULA

2. EXERCISE 12.2
Q1 A park in the shape of quadrilateral ABCD , has C
= 90, AB = 9m , BC = 12m, CD = 5m and AD = 8m.
How much area does it occupy?
A
8 m
D
9m
5 m
B 12 m
C

3. SOLUTION
Area of Δ BCD = ½ × BC × CD
= ( ½ × 12 × 5 ) m²
= 30 cm²
Using Pythagoras theorem, we have
BD² = BC² + CD²
BD² = 12² + 5²
BD² = 144 + 25
BD² = 169
BD = √169 = 13 m

4. For Δ ABD
Let a = 13m, b = 8m and c = 9m
Now, s = ½ ( a + b + c)
= ½ ( 13 + 8 + 9) m
= ½ × 30m
= 15 m
s – a = (15 -13) m = 2m
s – b = (15 - 8) m = 7 m
s − c = (15 − 9) m = 6 m
and
 Area of ΔABD = √s(s — a)(s —b)(s—c)
= √15 × 2 × 7 × 6 m²
= √3 × 5 × 2 × 7 × 2 × 3 m²

5. = √2 × 2 × 3 × 3 × 5 × 7 m²
= 2 × 3√35 m² (approx.)
= 6 × 5.9 m² (approx.)
 Required area = ABD +
BCD
= 35.4 m² + 30 m²
= 65.4 m²

6. Q2 Find the area of a quadrilateral ABCD in
which AB = 3 cm, CD = 4 cm, DA = 5 cm, and
AC = 5 cm.
5 cm
C
4 cm
3 cm
D
A B

7. SOLUTION
Area of Δ ABC = ½ × AB × BC
= ( ½ × 3 × 4) cm²
= 6 cm²
For Δ ACD:
Let a = 5 cm, b = 4 cm and c = 5 cm.
then,
s = ½ × (a + b + c)
s = ½ ( 5 + 4 + 5 ) cm
s = ½ × 14 cm
s = 7 cm

8. Now, s – a = ( 7 – 5 ) = 2 cm
s – b = ( 7 – 4 ) = 3 cm
s – c = ( 7 – 5 ) = 2 cm
Area of Δ ACD = √s(s — a)(s —b)(s—c)
= √ 7 (2) (3) (2)
= √ 2 × 2 × 3 × 7
= 2 × √3 ×√7
= 2 × √21
= 2 × 4.58 = 9.167 /
-
Area of quadrilateral ABCD = Area of ΔABC +
Area of Δ ACD
= 6 + (9.16) cm²
= 15.2 cm² (approx.)

9. Q3 Radha made a picture of aeroplane with
coloured paper as shown in Fig. 17.24. find
the total area of the paper used.
6 cm 6 cm
I
II
5 cm
6.5 cm
1.5 cm
1 cm 1 cm
2 cm
IV
V
III

10. SOLUTION
Area of region I :
Region I is enclosed by a triangle of sides a = 5 cm, b = 5 cm and c =1 cm