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The area of a quadrilateral is [[1]] when its diagonal is 26cm and the perpendiculars drawn to it from the opposite vertices are 12.8cm and 11.2cm.

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answer is 312 C M 2.

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Detailed Solution

The area of a quadrilateral is

312 c m 2

when its diagonal is 26cm and the perpendiculars drawn to it from the opposite vertices are 12.8cm and 11.2cm.
Let us take a quadrilateral ABCD, where AC=26cm, DL=12.8cm and BM=11.2cm.
Question Image

Also, we can see that area of quadrilateral ABCD=Area of triangle ADC + Area of triangle ABC.
Area of triangle =

12 × b × h

, where b is base and h is height.
So, in triangle ADC, AC=26cm and DL=12.8cm.
Area of triangle DAB=

12 × A C × D L

= 12 × 26 × 12.8 c m

= 166.4 c m 2

Likewise, in triangle ABC, BC=26cm and BM=11.2cm.
Area of triangle DCB

= 12 × B C × B M

= 12 × 26 × 11.2

= 145.6 c m 2

Thus, the area of the quadrilateral is

116.4 + 145.6 c m 2 = 312 c m 2

.
Hence, the correct answer is

312 c m 2

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