Question

(1) The diagonal AC of a quadrilateral ABCD is 6 cm and the perpendiculars, BM from the vertex B is 3 cm and DN from D is 5 cm, dropped on the same diagonal. Find the area of the quadrilateral ABCD​

Answer 1

Your answer is in the picture.

Answer 2

Answer:

Area of the quadrilateral ABCD is 24cm²

Step-by-step explanation:

Given Diagonal AC = 6cm

BM = 3cm

DN = 5cm

We have to find the area of the quadrilateral ABCD.

Area of atriangle =  $\frac{1}{2}$ × base × height

Take a triangles ABC, ACD

In ΔABC,

Area of ΔABC = $\frac{1}{2}$ × BM × AC

                        = $\frac{1}{2}$ × 3 × 6

                        = 3 × 3

                        = 9cm²

Area of ΔADC = $\frac{1}{2}$ × DN ×AC

                       = $\frac{1}{2}$  × 5 × 6

                      = 3× 5

                      = 15cm²

Area of Quadrilateral ABCD = Area of ΔABC  +  Area of ΔADC

                                              = 9 + 15

                                              = 24cm²

Therefore, Area of the quadrilateral ABCD is 24cm².