Question

The two parallel sides of a trapezium are 10cm and 22 cm. If its height is 12cm, what is its
area?

options
a) 190 sq.cm
b) 109 sq.cm
c) 192 sq.cm
d) 100 sq.cm​

Answer 1

Solution:-

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$\implies$ Here it is given in the question that the length of two parallel sides of a trapezium are 10 cm and 22 cm. It's height is also given that is 12 cm. Now the question has asked us to find out the area of the given trapezium. So, to find the area of the trapezium we need to apply the formula of area of trapezium that is a + b / 2 × h. The result which we will get after solving by applying the formula will be the area of the given trapezium.

ANSWER:-

☯ The area of the trapezium is 192 cm².

☯ Option C is correct.

GIVEN:-

» Parallel sides = 10 cm and 22 cm

» Height = 12 cm

TO FIND:-

⟾ Area of the trapezium = ?

FORMULA:-

❖ Area of trapezium = ½ (Sum of parallel sides) × height

SOLVING BY APPLYING THE FORMULA:-

• Finding the area of trapezium:-

➠ Area = ½ (10 cm + 22 cm) × 12 cm

➠ Area = ½ × 32 cm × 12 cm

➠ Area = ½ × 384 cm²

➠ Area = 1 × 384 cm² / 2

➠ Area = 384 cm² / 2 = 192 cm²

➠ Area = 192 cm²

Thus, we got the answer. The area of the trapezium is 192 cm².

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Answer 2

Given :

• First Parallel Side = 10cm
• Second Parallel Side = 22cm
• Height of Trapezium = 12cm

To Find :

• Area of Trapezium.

Solution :

✰ As we know that, Area of Trapezium is given by ½ × height × (sum of parallel sides) .So we will put the given values in the formula to find the Area of the Trapezium.

⠀

⠀⠀⠀⟼ ⠀⠀Area = ½ × H × (S1 + S2)

⠀⠀⠀⟼ ⠀⠀Area = ½ × 12 × (10 + 22)

⠀⠀⠀⟼ ⠀⠀Area = ½ × 12 × 32

⠀⠀⠀⟼ ⠀⠀Area = 6 × 32

⠀⠀⠀⟼ ⠀⠀Area = 192cm²

⠀

Thus Correct Option is C

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★ Additional Info :

Formulas Related to Area :

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Quadrilateral = ½ × diagonal × sum of perpendiculars
• Area of Polygon = sum of the area of all regions into which it is divided

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