Question

area of trapezium which equal non parallel sides is is 168 metre square if the length of the parallel sides are 36 metre and 20 metre find the length of non parallel sides.​

Answer 1

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☆ ANSWER:-

● Your answer is 10 meters.

(Length of each equal non-parallel lines)

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☆ EXPLANATION:-

▪︎ Given:-

• A trapezium.

• Length of parallel sides = 36m and 20m.

• Area of the trapezium = 168 meter².

• Non-parallel sides are equal.

▪︎ To Find:-

• The equal length of non-parallel sides.

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▪︎ Formula Used:-

• Area of trapezium,

$\sf= \frac{1}{2} (sum \: of \: parallel \: sides) \times height$

▪︎ Now,

• Let the height of the trapezium be x.

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▪︎ So ATQ:-

$\tt\mapsto \frac{1}{2}(36m + 20m) \times x = 168m {}^{2} \\ \\ \tt\mapsto \frac{1}{2} (56m) \times x = 168m {}^{2} \\ \\ \tt\mapsto \frac{x}{\cancel{2}} (\cancel56m) = 168m {}^{2} \\ \\ \tt\mapsto28m \: x = 168m {}^{2} \\ \\ \tt\mapsto \: x = \frac{168m {}^{2} }{28m} \\ \\ \tt\large\red{\fbox{\mapsto \: x = 6m}}$

${\small{\blue{\boxed{\therefore{Height\:of\:Trapezium \:Is\:6m.}}}}}$

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▪︎ Also,

• CP = QD.

• AND,

• AB = PQ = CD -(CP+QD)

(See the ATTACHMENT)

$\tt\mapsto \: 20m = 36m - (a + a) \\ \\ \tt\mapsto36m - 2a = 20m \\ \\ \tt\mapsto2a = 36m - 20m \\ \\ \tt\mapsto2a = 16m \\ \\ \tt\mapsto \: a = \frac{16m}{2} \\ \\ \tt\large\red{\fbox{\mapsto \: a = 8m}}$

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▪︎ Therefore,

• From above calculations we get the length of height (AP) and CP.

• So to find the value of non-parallel side (AC) we can apply pythagoras theorem as angle APC = 90°.

$\tt \mapsto(AC) {}^{2} = (AP) {}^{2} + (CP) {}^{2} \\ \\ \tt \mapsto AC {}^{2} = (6m) {}^{2} + (8m) {}^{2} \\ \\ \tt \mapsto {AC}^{2} = 36m {}^{2} + 64m {}^{2} \\ \\ \tt \mapsto {AC}^{2} = 100m {}^{2} \\ \\ \tt \mapsto {AC}^{\cancel{2} } = (10m) {}^{\cancel{2} } \\ \\ \tt \large\pink{\fbox{\mapsto \: AC = 10m}}$

${\small{\green{\boxed{\bold{\therefore{Non-Parallel\:Sides\:=\:10m.}}}}}}$

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