Question

The parallel sides of a trapezium are 9 cm and 15 cm. If the area is 96 cm^2 then its height is?

Answer 1

Step-by-step explanation:

area of trapezium = 1/2 × ( sum of parallel sides) × h

96² = 1/2 × ( 9+15) × h

9216 = 1/2 × 24 × h

9216 × 2/24 = h

768 = height

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Answer 2

AnswEr-:

• $\mathrm {\underline {\dag{\pink {The \: Height \: of \: Trapezium \:is \: 8cm \:.}}}}$

Explanation-:

$\mathrm {\bf{ Given-:}}$

• The parallel sides of a trapezium are 9 cm and 15 cm.

• The area is 96 cm².

$\mathrm {\bf{ To\:Find-:}}$

• The Height of Trapezium.

$\underline {\dag{\mathrm {\bf{ Solution \:of\:Question \:-:}}}}$

• $\boxed {\mathrm {\bf{\red{ Area \:of\:Trapezium \:-: \dfrac{1}{2} \times Height \times ( a + b) \:or\:Sum\:of\:Parallel \:Sides \:.}}}}$

$\mathrm {\bf{ Here-:}}$

• The parallel sides of a trapezium are 9 cm and 15 cm.

• The area is 96 cm².

• The Height of Trapezium is ??

Now , By Putting known Values in Formula of Area of Trapezium-:

• $\longrightarrow {\mathrm {\bf{ \dfrac{1}{2} \times ( 9 + 15) \times Height= 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ \dfrac{1}{2} \times 24 \times Height= 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ \dfrac{1}{\cancel {2}} \times \cancel {24} \times Height= 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ 12 \times Height= 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ Height= \dfrac{96}{12}}}}$

• $\longrightarrow {\mathrm {\bf{ Height=\dfrac {\cancel {96}}{\cancel {12}}}}}$

• $\underline{\red{\boxed {\mathrm {\bf{ Height= 8 \:cm}}}}}$

Hence ,

• $\mathrm {\underline {\dag{\pink {The \: Height \: of \: Trapezium \:is \: 8cm \:.}}}}$

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• $\mathrm {\bf{\large{ ♡Verification-:}}}$

As , We know that,

• $\boxed {\mathrm {\bf{\red{ Area \:of\:Trapezium \:-: \dfrac{1}{2} \times Height \times ( a + b) \:or\:Sum\:of\:Parallel \:Sides \:.}}}}$

$\mathrm {\bf{ Here-:}}$

• The parallel sides of a trapezium are 9 cm and 15 cm.

• The area is 96 cm².

• The Height of Trapezium is 8 cm

Now , By Putting known Values in Formula of Area of Trapezium-:

• $\longrightarrow {\mathrm {\bf{ \dfrac{1}{2} \times ( 9 + 15) \times 8 = 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ \dfrac{1}{2} \times 24 \times 8 = 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ \dfrac{1}{\cancel {2}} \times \cancel {24}\times 8 = 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ 12 \times 8 = 96cm^{2}}}}$

• $\longrightarrow {\mathrm {\bf{ 96cm^{2} = 96cm^{2}}}}$

Therefore,

• $\longrightarrow {\mathrm {\bf{ LHS = RHS}}}$

• $\longrightarrow {\mathrm {\bf{ Hence, \: Verified! }}}$

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