Question

The parallel sides of a trapezium are 5 m and 8 m and the perpendicular
distance between them is 10 m.
Find the area of the trapezium.​

Answer 1

Given :-

• One Parallel side of the trapezium = a = 5 m

• Other Parallel side of the trapezium = b = 8 m

• Distance between them/height = h = 10 m

To Find :-

• Area of the trapezium.

Solution :-

We know that,

$\leadsto\:\:\underline{\boxed{\pink{\mathtt{Area= \dfrac{1}{2}\times h \times (a+b) }}}}$

Now,

$\longmapsto\:\:\:\sf{A = \dfrac{1}{2} \times 10 \times (5+8)}$

$\longmapsto\:\:\:\sf{A = 5 \times 13}$

$\longmapsto\:\:\:\sf{A = 65\:m^2}$

∴ Area of the trapezium = 65 m²

Answer 2

Given:

• Parallel sides of the parallelogram are 5m and 8m.
• Perpendicular distance between the parallel sides, i.e., height of the trapezium is 10m.

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To find:

• Area of the trapezium.

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Solution:

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➲ As we have the length of both parallel sides of the parallelogram and height as well.

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Consider,

1. First parallel side = a
2. Second parallel side = b
3. Height = h

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Now,

• Formula for area of a trapezium is given as

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$\boxed{\large{\gray{\pmb{\bf{Area = \dfrac{a + b}{2} \times h}}}}}$

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Here,

• a = 5
• b = 8
• h = 10

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Substituting values in the formula

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$\tt:\implies{Area = \dfrac{5 + 8}{2} \times 10}$

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$\tt:\implies{Area = \dfrac{13}{\cancel{2}} \times \cancel{10}}$

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$\tt:\implies{Area = 13 \times 5}$

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$\bf:\implies{Area = 65}$

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Hence,

• Area of the trapezium is 65 m².

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