Question

the area average bases of a trapezium is 110 cm. find its area if its altitude is 80cm.​

Answer 1

Given,

The average area of the bases of a trapezium is 110 cm and its altitude is 80 cm.

To Find,

The area of the trapezium.

Solution,

Averages of the two bases of a trapezium is the mean of the two bases.

Let the two bases be a and b.

Given,

$\dfrac{a+b}{2}=110$

Area of a trapezium = $\dfrac{a+b}{2}\times\:height$

Where,

→ $\dfrac{a+b}{2}=110cm$

→ $height(altitude)=80cm$

Substituting the values,

110 x 80 = 8800cm²

Therefore, the area of the trapezium is 8800cm².

Formulas used:

→ Area of a trapezium

→ Finding the mean (average)

Knowledge Bytes:

→ Trapezium

A trapezium is a quadrilateral with one pair of opposite sides as parallel.

Answer 2

Given

• Average bases of a trapezium = 110cm.
• Attitude (height) of trapezium = 80cm.

⠀

To find

• Area of the Trapezium.

⠀

Solution

• In this question, average of base of a trapezium is given.

⠀

⠀⠀❍ Average of bases = Mean of bases

★ It can be written as :-

$\boxed{\sf{\orange{\dfrac{a + b}{2} = 110}}}$⠀⠀...[1]

⠀

⠀⠀❍ Formula used

$\boxed{\bf{\bigstar{Area_{(Trapezium)} = \dfrac{a + b}{2} \times height{\bigstar}}}}$

⠀

We have

• $\sf{\dfrac{a + b}{2} = 110}$

⠀

• $\sf{height = 80}$

⠀

Putting the values

$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(Trapezium)} = 110 \times 80}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(Trapezium)} = 8,800cm^2}$

⠀

Hence,

• Area of the Trapezium is 8,800 cm².

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