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Find the area of the trapezium in terms of x, and if $BCD = y$ , then calculate the value of y.

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105 x 2 s q . c m, 22.61 ∘

125 x 2 s q . c m, 34.51 ∘

235 x 2 s q . c m, 63.41 ∘

456 x 2 s q . c m, 87.31 ∘

answer is A.

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Detailed Solution

Let’s divide the field into two triangles ADF, BCE, and one rectangle ABEF.
Now, find the area of the triangle by using the formula

A = 12 × b × h

Area of ADF = 12 × D F × A F = 12 × 4 x × 5 x = 20 x 2 2 = 10 x 2 s q . c m .

Area of BCE = 12 × C E × B E = 12 × 12 x × 5 x = 60 x 2 2 = 30 x 2 s q . c m .

Now, calculate the value of the area of the rectangle by using the formula

A = l × b

Area of ABEF = A B × B E = 13 x × 5 x = 65 x 2 s q . c m .

Area of the trapezium ABCD = Area of triangle ADF+Area of triangle BCE+Area of rectangle ABEF =10x 2 +65x 2 +30x 2 =105x 2 sq .cm

To find the value of y, in right angled triangle at angle E, we have

tan y = o p p o s i t e a d j a c e n t = B E C E = 5 x 12 x = 512 y = tan − 1 512 y = 22.61 ∘

Hence, the correct option is 1.

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