Question

find the height of the Trapezium if it's area is 128 sq. cm and the length of the parallel sides are 18cm and 14cm​

Answer 1

⇝Given :-

• Area of trapezium = 128 cm²
• Length of 1st parallel side = 18 cm
• Length of 2nd parallel side = 14 cm

⇝To Find :-

• Height = ?

⇝Solution :-

${\red{❒}}{\underline{\bf{ We \: know \: that :}}}$

${\large{\red{\bigstar \: \: {\blue{\underbrace{\underline{\orange{\bf{Area \: {_{(trapezium)}}= \frac{1}{2} \times (a + b) \times H}}}}}}}}}$

${\red{❒}}{\underline{\bf{ Here :}}}$

• ➵ Area = 128 cm²
• ➵ A = 1st parallel side = 18 cm
• ➵ B = 2nd parallel side = 14 cm
• ➵ H = Height = ?

${\red{❒}}{\underline{\bf{ Finding \: Height :}}}$

${\large{\blue{:{➳}}}{\bf{ \: \: Area = \frac{1}{2} \times (a + b) \times h }}}$

${\large{\blue{:{➳}}}{\bf{ \: \: \: 128 = \frac{1}{2} \times (18 + 14) \times h }}}$

${\large{\blue{:{➳}}}{\bf{ \: \: \: 128 = \frac{1}{2} \times 32\times h }}}$

${\large{\blue{:{➳}}}{\bf{ \: \: \: {\cancel \frac{128}{32} } = \frac{1}{2} \times h }}}$

${\large{\blue{:{➳}}}{\bf{ \: \: \: 4= \frac{1}{2} \times h }}}$

${\large{\blue{:{➳}}}{\bf{ \: \: \: 4 \times 2 = 1 \times h }}}$

${\large{\purple{:{\longmapsto{\underline{\overline{\boxed{\bf{ H = 8 \: cm}}}}}}}}}$

${\red{❒}}{\underline{\bf{ Therefore:}}}$

${\large{\orange{\underline{\green{\underline{\red{\mathfrak{Height = 8 cm}}}}}}}}$

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