Question

the area of trapezuim is 800 cm square .the distance between the parallel wide is 20 cm.one parallel side is 45 cm find other side​

Answer 1

Given :

• Area of Parallelogram = 800 cm²
• Distance between the parallel sides = 20 cm
• One of the parallel side = 45 cm

To Find :

Measure of the other parallel side.

Solution :

Analysis :

Here we have to use the area of Trapezium formula.

Required Formula :

Area of Trapezium = ½ × (a + b) × d

where,

• a & b = two parallel sides
• d = distance between them

Explanation :

Let the other side be “b” cm.

We know that if we are given the area if trapezium, distance between the two parallel sides and one of the parallel side and is asked to find the other one then our required formula is,

Area of Trapezium = ½ × (a + b) × d

where,

• a = 45 cm
• Area = 800 cm²
• d = 20 cm
• b = b cm

Using the required formula and substituting the required values,

⇒ Area of Trapezium = ½ × (a + b) × d

⇒ 800 = ½ × (45 + b) × 20

⇒ 800 = 1 × (45 + b) × 10

⇒ 800 = (45 + b) × 10

⇒ 800/10 = (45 + b)

⇒ 80/1 = (45 + b)

⇒ 80 = (45 + b)

⇒ 80 = 45 + b

⇒ 80 - 45 = b

⇒ 35 = b

∴ b = 35 cm.

The other parallel side is 35 cm.

Verification :

LHS :

⇒ Area of Trapezium

⇒ 800

∴ 800 cm².

RHS :

⇒ ½ × (a + b) × d

⇒ ½ × (45 + 35) × 20

⇒ 1 × (45 + 35) × 10

⇒ (45 + 35) × 10

⇒ (80) × 10

⇒ 80 × 10

⇒ 800

∴ 800 cm².

∴ LHS = RHS.

• Hence verified.

Explore More :

• Perimeter of rectangle = 2(Length + Breadth)
• Area of rectangle = Length × Breadth
• Perimeter of square = 4 × side
• Area of square = side × side

Answer 2

Correct Question-:

• The area of trapezuim is 800 cm² . The distance between the parallel side is 20 cm. If one parallel side is 45 cm then , Find other side?

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{The\:other\:Parallel \:side\:be\:=\frak{35\:cm.}}}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\:area\:of\:Trapezium \:\:is\:= \frak{800cm²}} & \\\\ \sf{One\:of\:the\:Parallel \:Side\:\:=\:\frak{45cm}}& \\\\ \sf{Altitude\:or\:Distance \:between\:Parallel \:Side\:is\:=\:\frak{20cm}}\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{ The\:other\:Parallel \:side.}\end{cases}$

Solution-:

• $\frak{Let's \:Assume \: -:} \begin{cases} \sf{ The\:other\:Parallel \:side\:be\:\frak{x\:cm}}\end{cases}$

• $\underline{\boxed{\star{\sf{\blue{Area \:of\:Trapezium \: =\frac{1}{2} × Altitude × (a +b) \:or\:Sum\:of\:Parallel \:sides.  .}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{The\:area\:of\:Trapezium \:\:is\:= \frak{800cm²}} & \\\\ \sf{One\:of\:the\:Parallel \:Side\:or\:A=\:\frak{55cm}}& \\\\ \sf{Altitude\:or\:Distance \:between\:Parallel \:Side\:is\:=\:\frak{20cm}}& \\\\ \sf{ The\:other\:Parallel \:side\:is\:\frak{x\:cm}}\end{cases}$

Now ,

• $\implies{\sf{\large {800 cm² = \frac {1}{2} \times 20 \times (45 + x)}}}$
• $\implies{\sf{\large {800 cm² = 10 \times (45 + x)}}}$
• $\implies{\sf{\large {\frac{800}{10} = 45 + x}}}$
• $\implies{\sf{\large {80 = 45 + x}}}$
• $\implies{\sf{\large {80-45 = x}}}$
• $\implies{\sf{\large {35 = x}}}$

Therefore-:

• $\underline{\boxed{\star{\sf{\blue{  \:x = 35 cm.}}}}}$

Then ,

• $\frak{Putting \:x =35 \: -:} \begin{cases} \sf{ The\:other\:Parallel \:side\:be\:= x=\frak{35\:cm}}\end{cases}$

HENCE ,

• $\underline{\boxed{\star{\sf{\blue{The\:other\:Parallel \:side\:be\:=\frak{35\:cm.}}}}}}$

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♤ Verification ♤

• $\underline{\boxed{\star{\sf{\blue{Area \:of\:Trapezium \: =\frac{1}{2} × Altitude × (a +b) \:or\:Sum\:of\:Parallel \:sides.  .}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{The\:area\:of\:Trapezium \:\:is\:= \frak{800cm²}} & \\\\ \sf{One\:of\:the\:Parallel \:Side\:or\:A=\:\frak{45cm}}& \\\\ \sf{Altitude\:or\:Distance \:between\:Parallel \:Side\:is\:=\:\frak{20cm}}& \\\\ \sf{ The\:other\:Parallel \:side\:is\:\frak{35\:cm}}\end{cases}$

Then ,

• $\implies{\sf{\large {800 cm² = \frac {1}{2} \times 20 \times (45 + 35)}}}$
• $\implies{\sf{\large {800 cm² = 10 \times (45 + 35)}}}$
• $\implies{\sf{\large {800 cm² = 10 \times (80)}}}$
• $\implies{\sf{\large {800 cm² = 800cm²}}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{  LHS \: =RHS.}}}}}$

• $\underline{\boxed{\star{\sf{\blue{ Hence,\: =Verified.}}}}}$

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