Find the area of the quadrilateral (in sq.units) as shown in the figure below. $∠$ EAB = $∠$ AED = 90°. Given that: AB + AE = 4 units and EC = 7 units.

22

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Solution

The correct option is A 22
Drop BD $⊥$ EC.
Realise that $△$ BDC is a right angled triangle and so we need not use Heron's formula.
So, area of ( $△$ BDC) = $\frac{1}{2}$ $\times$ BD $\times$ DC = $\frac{1}{2}$ $\times$ 4 $\times$ 3 = 6 square units.
Area of (ABDE) = $4^{2}$ = 16 square units.
So, area = 16 + 6 = 22 square units.

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Find the area of the quadrilateral (in sq.units) as shown in the figure below. ∠EAB = ∠AED = 90°. Given that: AB + AE = 4 units and EC = 7 units. 22

The correct option is A 22Drop BD⊥EC. Realise that △BDC is a right angled triangle and so we need not use Heron's formula. So, area of (△BDC) = 12 × BD × DC = 12 × 4 × 3 = 6 square units. Area of (ABDE) = 42 = 16 square units. So, area = 16 + 6 = 22 square units.

Find the area of the quadrilateral (in sq.units) as shown in the figure below. $∠$ EAB = $∠$ AED = 90°. Given that: AB + AE = 4 units and EC = 7 units.

22