What is the height of roof i.e., DE?

Question

Riya and her sister visited their friend’s farmhouse. Upon arrival, Riya noticed that the roof of her friend’s house was shaped like a trapezium, with the dimensions indicated in the figure.

On the basis of above information, answer the following questions:

(i) What is the height of roof i.e., DE?

Smart Achievers · Accepted Answer

(3)

$G i v e n, A B C D i s t r a p e z i u m w i t h A B ∥ C D . C D = 8 m, ∠ D A E = 30 ° a n d A D = B C = 6 m W e h a v e t o f i n d t h e h e i g h t o f r o o f i . e ., h e i g h t o f t r a p e z i u m (D E o r C F) . I n △ A E D, r i g h t a n g l e d a t E, w e h a v e i n ∠ D A E = \frac{D E}{A D} \Rightarrow s i n 30 ° = \frac{D E}{6} [∵ ∠ D A E = 30 ° and A D = 6 m] \Rightarrow \frac{1}{2} = \frac{D E}{6} \Rightarrow D E = 3 m Hence, height of roof is 3 m .$

Solution

1 1 m

2 5 m

3 3 m

4 2 m

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