Question

EXERCISE 12.2
+
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?​

Answer 1

Step-by-step explanation:

4️⃣ 32 cmHere, AB = 9 m, BC = 12 m, CD = 5 m, DA = 8 m.

And BD is a diagonal of ABCD.

In right △BCD,

From Pythagoras theorem;

BD2 = BC2 + CD2

BD2 = 122 + 52

= 144 + 25

= 169

BD = 13 m

Area of △BCD = 1/2 x BC x CD

= 1/2 x 12 x 5

= 30

Area of △BCD = 30 m2

Now, In △ABD,

All sides are known, Apply Heron’s Formula:

Where a, b and c are sides of a triangle.

Perimeter of △ABD = 2s = 9 m + 8m + 13m

s = 15 m

Area of the △ABD = 35.49 m2

Area of quadrilateral ABCD = Area of △ABD + Area of △BCD

= (35.496 + 30) m2

= 65.5 m