Question

find the area of a quadrilateral whose diagonal is of length 70 metre and lengths of the perpendicular drawn from the opposite vertices on the diagonal are of length 42 metre and 50 metre respectively​

Answer 1

Step-by-step explanation:

Area=

2

1

×One diagonal×Sum of the length of the perpendiculars drawn from it on the remaining two vertices.

=

2

1

×70×(42+50)

=35×92=3220‬sq.m

Answer 2

Given :-

• Length of diagnol = 70 m
• Lengths of perpendicular = 42 m and 50 m

To Find :-

• Area of quadrilateral

Solution :-

➩ Area of quadrilateral = (½) × diagonal × sum of the length of the perpendiculars

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We are given all the values so by simply substituting the value in formula we can find the area of quadrilateral -

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⠀

➩ $\sf Area\: of \:quadrilateral = \frac{1}{2} \times diagnol \times ( sum \:of\: the\: length \:of \:the \:perpendiculars )$

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➩ $\sf Area = \frac{1}{2} \times 70 \times ( 42 + 50 )$

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➩ $\sf Area = \frac{1}{2} \times 70 \times 92$

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➩ $\sf Area = \frac{1}{\cancel 2} \times \cancel 70 \times 92$

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➩ $\sf Area = 35 \times 92$

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➩ $\sf Area = 3220$

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$\boxed{\sf\red{Area\: of\: quadrilateral = 3220 \:m^2}}$