Question

Calculate the area of quadrilateral A B C D when length of the diagonal AC=10cm and the length of perpendicular from B and D on AC be 5cm and 6 cm respectively.

Answer 1

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Answer 2

Area of quadrilateral ABCD is 55 square centimetres.

Step-by-step explanation:

Refer to the attached figure,

Given:- In Quadrilateral ABCD,

AC = 10 cm, BF = 5 cm, DE = 6 cm.

To find:- Area of quadrilateral ABCD = ?

Solution:-

From attached figure we can see that,

Area of $\triangle ABC$ = $\frac{1}{2} \times b\times h$

where b is the base and h is the height of $\triangle ABC$.

b = AC = 10 cm   -----------(given)

h = BF = 5 cm     -----------(given)

$\therefore$ Area of $\triangle ABC$ = $\frac{1}{2} \times 10\times 5$

= $\frac{1}{2} \times 50$

$\therefore$ Area of $\triangle ABC$ = 25 square centimetres.

Now,

Area of $\triangle ADC$ = $\frac{1}{2} \times b\times h$

where b is the base and h is the height of $\triangle ADC$ .

b =AC = 10 cm, and h = DE = 6 cm  -------------(given)

$\therefore$ Area of $\triangle ADC$ = $\frac{1}{2} \times 10\times 6$

$=\frac{1}{2}\times 60$

$\therefore$ Area of $\triangle ADC$ = 30 square centimetres.

Now, from attached figure we can see that,

Area of Quadrilateral ABCD = Area of $\triangle ABC$ + Area of $\triangle ADC$

$\therefore$ Area of Quadrilateral ABCD = 25 +30

$\therefore$ Area of Quadrilateral ABCD = 55 square centimetres.