Question

find the area of quadrilateral one of whose diagonals is 40 cm and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are 16 cm and 12 cm

Answer 1

Area of quadrilateral= 1/2 × diagonal( Some of perpendiculars )

Area = 1/2 × 40cm × (16+12) cm
Area = 1/2 × 40cm × 28 cm
Area = 20 cm× 28 cm
= 560cm^2

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Answer 2

Given,

Length of the diagonal of a quadrilateral = 40 cm

The lengths of the perpendiculars drawn from the opposite vertices on the diagonal are 16 cm and 12 cm.

To find,

The area of the quadrilateral.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The area of a quadrilateral

= 1/2 × (length of the diagonal) × (sum of the length of the perpendiculars drawn from the opposite vertices on the diagonal)

{Statement-1}

Now, according to the question and statement-1;

The area of the quadrilateral

= 1/2 × (length of the diagonal) × (sum of the lengths of the perpendiculars drawn from the opposite vertices on the diagonal)

= 1/2 × (40 cm) × (16 cm × 12 cm)

= 1/2 × (40 cm) × 28 cm

= 560 cm^2

Hence, the area of the quadrilateral is equal to 560 cm^2.