Question

Work out the area of a trapeziums whose height is8 cm and the parallel sides measure 14 cm and 17 cm

Answer 1

Given :-

Parallel sides of trapezium is 14cm and 17 cm

Height of trapezium is 8cm

To find :-

The area of trapezium

A.T.Q:-

$\boxed{\sf{Area\:of\: trapezium=\dfrac{1}{2}\times height\times (sum\:of\: parallel\:sides)}}$

Now find the Area

$\sf\implies Area_{trapezium}=\dfrac{1}{2}\times 8\times (17+14)\\ \\ \sf\implies Area=\dfrac{1}{\cancel2}\times \cancel{8}\times 31\\ \\ \sf\implies Area= 4\times 31\\ \\ \sf\implies Area = {124cm}^{2}$

$\underline{\sf{\dag{\:\:Area\:of\: trapezium=124cm{}^{2}}}}$

$\bf{\underline{Some \:extra \:informations :-}}$

$\sf\bullet Area \:of \:parallelogram= Base\times Height \\ \\ \sf\bullet Area \:of\: rhombus =\dfrac{1}{2}\times d_1\times d_2\\ \\ \sf\bullet Area\: of \:quadrilateral= \dfrac{1}{2}\times d(h_1+h_2)$

Answer 2

$\huge{\underline{\underline{\red{Answer}}}}$

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$\mathbb{\boxed{\pink{GIVEN}}}$

• height= 8cm
• parallel sides = 14cm and 17cm.

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$\mathbb{\boxed{\pink{NEED\:TO\:FIND}}}$

• Area of the trapizium=?

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let the parallel sides be a and b

and let the height be h

then according to the question,

• a=14cm
• b=17cm
• h=8cm

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We know,

Area of a trapixium is:

$\frac{1}{2} \times (sum \: of \: parallel \: sides) \times height \\ \implies \frac{1}{2} \times (a + b)h \\ \implies \frac{1}{2} \times (14 + 17) \times 8 {cm}^{2} \\ \implies \: 4 \times 31 {cm}^{2} \\ \implies \: 124 {cm}^{2}$

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Thus the area is $\large{\boxed{\bold{\red{124}{cm^{2}}}}}$