Question

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Answer 1

Answer:

Length of the equal non-parallel sides is 12.65 cm and Perimeter of the trapezium is 63.3 cm.

Step-by-step explanation:

QUESTION :

• The area of a trapezium with equal non - parallel sides is 228 cm². If the lengths of parallel sides are 10 cm and 28 cm, then find the length of the non-parallel sides and perimeter of the trapezium.

ANSWER :

Given :

• Area of trapezium is 228 cm².
• Non - parallel sides of the trapezium are equal.
• Length of parallel sides are 10 cm and 28 cm.

To find :

• Length of the non-parallel sides.
• Perimeter of the trapezium.

Solution :

Suppose, ABCD is a trapezium having height h and non-parallel sides BC and AD.

• We have to find non-parallel sides of the trapezium. For finding them we need height of trapezium. We will find height using area of the trapezium. Formula is :

• $\pmb{\sf Area \: of \: trapezium = \dfrac{Sum \: of \: parallel \: sides}{2} \times height }$

Put values in formula :

$\implies \sf 228 = \dfrac{10 + 28}{2} \times h$

$\implies \sf 228 = \dfrac{38}{2} \times h$

$\implies \sf 228 = 19 \times h$

$\implies \sf h = \dfrac{228}{19}$

$\implies \pmb{\sf h = 12}$

Height of trapezium is 12 cm.

• DO is 4 cm beacuse if we construct perpendiculars h and PB. Then ABPO will be rectangle and measure of PO will be 10 cm and measure of PC and DO will be 4 cm and 4 cm respectively.
• Now, ∆AOD is right angled triangle at O. Height of trapezium (h) is perpendicular of ∆AOD. And AD, non-parallel side is hypotenuse and DO is base. So,

By Pythagoras theorem :

• (Hypotenuse)² = (Base)² + (Perpendicular)²

$\implies \sf (AD)^{2} = (DO)^{2} + (h)^{2}$

$\implies \sf AD^{2} = (4)^{2} + (12)^{2}$

$\implies \sf AD^{2} = 16 + 144$

$\implies \sf AD^{2} = 160$

$\implies \sf AD = \sqrt{160}$

$\implies \pmb{\sf AD = 12.65}$

Length of AD is 12.65 cm.

• AD is one non-parallel side of trapezium. And it is given that non-parallel sides of trapezium are equal. So, Length of BC is also 12.65 cm.

Thus,

Length of equal non-parallel sides is 12.65 cm.

Now,

• Perimeter of trapezium = Sum of all sides

$\implies \sf Perimeter = 10 + 28 + 12.65 + 12.65$

$\implies \sf Perimeter = 63.3$

Therefore,

Perimeter of the trapezium is 63.3 cm.