Question

1. Find the area of the quadrilateral ABCD, in which AC = 36 cm. BL and DM
are perpendiculars from B and D to AC whose lengths are 16 cm and 18 cm
respectively
18 cm
36 cm
16 cm
M​

Answer 1

Given:-

• Diagonal AC is 36 cm.

• Perpendiculars from B and D to AC is 16 cm and 18 cm respectively.

To Find:-

• Area of quadrilateral.

Solution:-

Here, We have to find the area of quadrilateral ABCD.

∵ Area of quadrilateral ⇒ $\dfrac{1}{2} \times D \times ( p_{1} + p_{2})$

        Where, D = diagonal length

                     p₁ and p₂ = Perpendicular drawn from remaining two vertices.

Now, Area of quadrilateral ⇒ $\dfrac{1}{2} \times D \times ( p_{1} + p_{2})$

                                             ⇒ $\dfrac{1}{2} \times 36 \ cm \times ( 16 \ cm + 18 \ cm)$

                                             ⇒ $\dfrac{1}{2} \times 36 \ cm \times 34 \ cm$

                                             ⇒ 612 cm²

Hence, Area of quadrilateral ABCD is 612 cm².

Some Imporatant Terms:-

• Area of Parallelogram = Base × Height

• Area of Square = Side²

• Area of Rectangle = Length × Breadth

• Area of Triangle = $\dfrac{1}{2} \times Base \times Height$