Question

Find the area of a quadrilateral whose diagonal is 23cm and a perpendicular dropped on it from opposite vertices are 6cm and 8cm. ​

Answer 1

Answer:

Given AC=25 cm,BE=3.6 cm,DF=2.4 cm

Area of quadrilateral = area of △ABC+ area of △ACD

=(

2

1

×AC×BE)+(

2

1

×AC×DF)

=(

2

1

×25×3.6)+(

2

1

×25×2.4)

=

2

90

+

2

60

=45+30=85

∴ Area of quadrilateral =85 cm

2

Answer 2

Given,

Length of the diagonal of a quadrilateral = 23 cm

The length of the perpendiculars dropped on it from the opposite vertices are 6cm and 8cm.

To find,

The area of the quadrilateral.

Solution,

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

Mathematically,

Area of a quadrilateral

= (½) × (length of a diagonal) × (sum of the length of the perpendiculars drawn from the two opposite vertices)

{Statement-1}

Now, according to the question;

The area of the quadrilateral

= (½) × (length of a diagonal) × (sum of the length of the perpendiculars drawn from the two opposite vertices)

{according to Statement-1}

= (½) × (23 cm) × (8 cm + 6 cm)

= (½) × (23 cm) × (14 cm)

= (23×7) cm^2

= 161 cm^2

Hence, the area of the quadrilateral is equal to 161 cm^2.