Question

find the area of each of the following figure

Answer 1

SOLUTION :

(i)

let it name be ABCD quadrilateral

Draw CE║AB   [∴ AB = CE, each 9 ]

Now,

∠EAB = ∠ABC = ∠BCE = ∠CEA, each 90°

also, ∠DEC = 90°

here,

we get two different figures, square ABCE and triangle CDE

Area of square = $\sqrt{(side)}^{2}$    

Area of the square =  $\bf 9^{2}=81$

Now area of the triangle = $\bf \frac{1}{2} \times base \times height$

= $\bf \frac{1}{2} \times 9 \times 4 = 18$

Area of quadrilateral ABCD = Area of square + Area of triangle

= 81 + 18 = 99

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(ii)

Let its name be quadrilateral ABCDE

Draw CE║AB     [ ∴ AB = CE ]

BC = AE each 6

CD = 3, DE = 4

∠CDE = 90°

Here we got two shapes, Rectangle and triangle

Area of the rectangle = lb    [∵ In which l is the length and b is the breadth of the rectangle ]

Area of the rectangle = 6 × 5 = 30

Now, area of the triangle = $\bf \frac{1}{2} \times base \times height$

=$\bf \frac{1}{2} \times 3 \times 4 = 6$

Area of ABCDE = area of rectangle + area of triangle

= 30 + 6 = 36

Hence

(i) Ans- 99

(ii) Ans- 36