Question

the area of a Trapezium is 192 cm square if its altitude is 16 cm and one of the parallel sides is 8 cm long what is the length of other parallel side​

Answer 1

$\huge\mathbb{ANSWER}$

$\boxed{The\:length\:of\:other\:parallel\:side\:is\:16cm}$

$\huge\mathbb{SOLUTION}$

Given,

• Area of trapezium = 192 cm²
• Altitude of trapezium = 16 cm
• One of the parallel side of trapezium = 8 cm

To Find,

• Length of the other parallel side = ?

According To The Question,

First of all, area of trapezium = 1/2(a+b)h

Here, "a" is one parallel side and "b" is the other parallel side and "h" is the height.

Now,

→ Area of trapezium = 1/2(a + b)h

We will put the values/things which are mentioned in the question.

→ 192 cm² = 1/2(8 + b)16

→ 192 cm² = (8 + b)8

→ 192 cm² = 16 + 8b

→ 192 cm² - 16 = 8b

→ 128 cm = 8b

→ 128/8 = b

After cancelling 128 and 8, we got our answer :

→ 16 cm = b

________________________

Extra Information :

• Area of rectangle = L × B
• Area of square = (Side)²
• Area of rhombus = 1/2(product of its diagonals)

Answer 2

$\bf{\underline{\underline{\bf{Given\::}}}}}$

The area of a trapezium is 192 cm² if its altitude is 16 cm and one of the parallel sides is 8 cm long.

$\bf{\underline{\underline{\bf{To\:find\::}}}}}$

The length of the other parallel side.

$\bf{\underline{\underline{\bf{Explanation\::}}}}}$

We know that formula of the area of trapezium :

$\bf{\boxed{\bf{Area\:of\:trapezium=\frac{1}{2} \times (sum\:of\:base)\times height}}}}}$

$\bf{We\:have}\begin{cases}\sf{The\:area\:of\:trape.=192cm^{2} }\\ \sf{The\:height\:of\:trape.(h)=16cm}\\ \sf{One\:parallel\:of\:the\:base\:(a)=8cm}\end{cases}}$

A/q

$\implies\tt{192cm^{2} =\dfrac{1}{2} \times (8+b)\times 16cm}\\\\\\\implies\tt{(192\times 2)cm^{2} =(8+b)\times 16cm}\\\\\\\implies\tt{384cm^{2} =(8+b)\times 16cm}\\\\\\\implies\tt{\cancel{\dfrac{384cm^{2} }{16cm} }=(8+b)}\\\\\\\implies\tt{24cm=8cm+b}\\\\\\\implies\tt{b=(24-8)cm}\\\\\\\implies\tt{\red{b=16\:cm}}$

Thus,

The length of the other parallel side is 16 cm.