Question

The diagonal of quadrilateral is 16 cm long and the perpendicularars drawn to it from the opposite vertices are 5.5cm and 6.5cm . Find the area of the quadrijateral

Answer 1

Answer:

96Cm^2

Step-by-step explanation:

Let,ABCD is a quadrilateral with one of its diagonal AC=16cm DM and BN are two perpendiculars on AC such that DM=6.5cm and BN=5.5cm.

ar(ABCD)=ar(BAC)+ar(DAC)

               =1/2*16*5.5 + 1/2*16*6.5

               =1/2*16(5.5+6.5)

               =8*(12)

               =96 cm^2

Answer 2

The the area of quadrilateral is 96 cm².

Let ABCD be a quadrilateral with one of its diagonal AC = 16cm (Given)

AE = 6.5cm (Given)

CF = 5.5cm (Given)

Area of (ABCD) = Area of Δ(ADB) + Area of Δ (BCD)

= 1/2 × 16 × 5.5 + 1/2 × 16 × 6.5

= 1/2 × 16 (5.5+6.5)

= 8 × 12

= 96

Therefore, the area of quadrilateral is 96 cm².