Question

160 m
100m
80 m
or,
с C
Fig. 12.14
1. A park, in the shape of a quadrilateral ABCD, has Z C = 90°, AB = 9 m, BC = 12 m,
26 Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm,
Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find
Alternative method : Draw CE I BD (see Fig. 12.14).
А A
As BD = 160 m, we have
DE = 160 m -2 = 80 m
And, DE2 + CE2 = DC?, which gives
CE =
DC2 – DE
CE = V1002 – 80?m= 60 m
Therefore, area of A BCD = 7x160x60 m² = 4800 m2
2
EXERCISE 12.2
CD= 5 m and AD = 8 m. How much area does it occupy?
DA= 5 cm and AC=5 cm.
the total area of the paper used.​

Answer 1

As BD = 160 m, we have
DE = 160 m -2 = 80 m
And, DE2 + CE2 = DC?, which gives
CE =
DC2 – DE
CE = V1002 – 80?m= 60 m
Therefore, area of A BCD = 7x160x60 m² = 4800 m2
2
E

Answer 2

Solution:

Given a quadrilateral ABCD in which ∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m & AD = 8 m.

Join the diagonal BD which divides quadrilateral ABCD in two triangles i.e ∆BCD & ∆ABD.

In ΔBCD,

By applying Pythagoras Theorem

BD²=BC² +CD²

BD²= 12²+ 5²= 144+25

BD²= 169

BD = √169= 13m

∆BCD is a right angled triangle.

Area of ΔBCD = 1/2 ×base× height

=1/2× 5 × 12= 30 m²

For ∆ABD,

Let a= 9m, b= 8m, c=13m

Now,

Semi perimeter of ΔABD,(s) = (a+b+c) /2

s=(8 + 9 + 13)/2 m

= 30/2 m = 15 m

s = 15m

Using heron’s formula,

Area of ΔABD = √s (s-a) (s-b) (s-c)

= √15(15 – 9) (15 – 9) (15 – 13)

= √15 × 6 × 7× 2

=√5×3×3×2×7×2

=3×2√35

= 6√35= 6× 5.92

[ √6= 5.92..]

= 35.52m² (approx)

Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD

= 30+ 35.5= 65.5 m²

Hence, area of the park is 65.5m²