Question

find the area of a quad. abcd in which ab=9m, bc=40m,cd=28m ad=15m&angle B= 90

Answer 1

Answer:

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

Answer

Given in the question

∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m

BD is joined.

Area of the quadrilateral ABCD can be found using the area of the separate triangle and then adding up

In ΔBCD,

By applying Pythagoras theorem,

BD2 = BC2 + CD2  

BD2 = 122 + 52  

BD2 = 169

BD = 13 m

Area of ΔBCD=Area of right angle triangle= (1/2) × base × Height

So Area of ΔBCD = 1/2 × 12 × 5 = 30 m2

Now,

Semi perimeter of ΔABD(s) = (8 + 9 + 13)/2 m = 30/2 m = 15 m

Using heron's formula,

Area of ΔABD  = √s (s-a) (s-b) (s-c)

                                      = √15(15 - 13) (15 - 9) (15 - 8) m2

                                      = √15 × 2 × 6 × 7 m2

                                      = 6√35 m2 = 35.5 m2 (approx)

Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD = 30 m2 + 35.5m2 = 65.5m2