Question

The area of trapezium is 540cm sqare.
If the length of its parallel sides are 42cm and 66cm , find the perpendicular distance between them.
Please help me

Answer 1

Answer:

Perpendicular distance = 10 cm

Step-by-step explanation:

Given:

• Area of trapezium = 540 cm²
• Length of its parallel sides = 42 cm and 66 cm

To find:

☞ The perpendicular distance between them (height) = ?

Formula used:

$\maltese \: \: \red{ \boxed{ \sf{Area \: of \: trapezium = \dfrac{1}{2} \times (a + b) \times h}}}$

where:

• a and b are the lengths of parallel sides.
• h is the perpendicular distance between them.

Solution:

Applying the above formula and substituting the values,

$\mapsto \: \: \sf{540 = \dfrac{1}{2} \times (42 + 66) \times h}$

$\implies \sf{540 = \dfrac{1}{2} \times (108) \times h }$

$\implies \sf{540 = \dfrac{108}{2} \times h}$

$\implies \sf{54h = 540}$

$\implies \sf{h = \dfrac{540}{54} }$

$\therefore \: \boxed{ \boldsymbol{height = 10 \: cm}}$

Hence, Perpendicular distance between the parallel lines = 10 cm

Answer 2

Question :-

The area of trapezium is 540cm sqare.

If the length of its parallel sides are 42cm and 66cm , find the perpendicular distance between them.

Answer :-

• The perpendicular distance between them is 10cm.

Step by step explanation :-

Given that,

• Area of trapezium is 540cm²
• Lengths of parallel sides are 42cm and 66cm.

We know that,

$\rm:\leadsto{Area_{(Trapezium)} = \frac{a + b}{2}.h }$

We have,

• a = 42cm
• b = 66cm
• A = 540cm²

Substituting all values in formula,

$\rm:\longmapsto{540 = \frac{42 + 66}{2} \times h} \\ \\ \rm:\longmapsto{540 = \frac{108}{2} \times h} \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{540 = 54 \times h} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{h = \frac{540}{54} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{h = 10cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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