Question

the height of trapezium of area 162cm square is 6cm. if one of the bases is 23 cm find the other

Answer 1

Answer:

• 31cm is the required answer

Step-by-step explanation:

According to the Question

It is given that

• Area of Trapezium = 162cm²
• Height of trapezium ,h = 6cm
• One base is 23 cm

Let the another base is b cm.

As we know that ,

•Area of trapezium = 1/2 × sum of bases × height

Substitute the value we get

→ 162 = 1/2× (23+b) × 6

→ 162×2 = (23+b) ×6

→ 324 = (23+b) × 6

→ 324/6 = 23+b

→ 54 = 23 + b

→ 54-23 = b

→ 31 = b

→ b = 31 cm

• Hence, the another base of the Trapezium is 31cm

Answer 2

Answer:

Given :-

• The height of trapezium of area is 162 cm² is 6 cm.
• One of the bases is 23 cm.

To Find :-

• What is the other base of trapezium.

Formula Used :-

$\clubsuit$ Area of trapezium Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Trapezium)} =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides \times Height}}}$

Solution :-

Let,

$\mapsto \sf\bold{\purple{Other\: base\: of\: trapezium =\: a\: cm}}$

Given :

$\leadsto \: \bf{Area\: of\: trapezium =\: 162\: cm^2}$

$\leadsto \: \bf{One\: of\: base\: of\: trapezium =\: 23\: cm}$

According to the question by using the formula we get,

$\longrightarrow \sf 162 =\: \dfrac{1}{2} \times \{23 + a\} \times 6$

$\longrightarrow \sf \dfrac{\cancel{162}}{\cancel{6}} =\: \dfrac{1}{2} \times \{23 + a\}$

$\longrightarrow \sf \dfrac{27}{1} =\: \dfrac{1}{2} \times \{23 + a\}$

$\longrightarrow \sf 27 =\: \dfrac{1}{2} \times \{23 + a\}$

$\longrightarrow \sf 27 \times 2 =\: 23 + a$

$\longrightarrow \sf 54 =\: 23 + a$

$\longrightarrow \sf 54 - 23 =\: a$

$\longrightarrow \sf 31 =\: a$

$\longrightarrow \sf\bold{\red{a =\: 31\: cm}}$

${\small{\bold{\underline{\therefore\: The\: other\: base\: of\: trapezium\: is\: 31\: cm\: .}}}}$