Question

The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?

A) 35 B) 75 C) 150 D) 225

Answer 1

✯ ANSWER ✯

• (C) 150 cm² (✔)

GIVEN:

• Length of parallel sides of trapezium are 21 cm and 9 cm.
• Height(h) of the trapezium is 10 cm

TO FIND:

• What is the area of the trapezium ?

SOLUTION:

We have given that, the lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm.

We know that the formula for finding the area of the trapezium is:-

$\bf{\star \: Area = \dfrac{1}{2} \times (Sum \: of \: parallel \: sides) \times height \: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow Area = \dfrac{1}{2} \times (21 + 9) \times 10}$

$\rm{\dashrightarrow Area = \dfrac{1}{\cancel{2}} \times \cancel{30} \times 10}$

$\rm{\dashrightarrow Area = 15 \times 10}$

$\bf{\dashrightarrow Area = 150 \: cm^2}$

❝ Hence, the area of trapezium is 150 cm² ❞

______________________

✰ Extra Information ✰

➣ The midline of a trapezium is parallel to the bases.

➣ The length of the midline of a trapezium is one half the sum of the lengths of the bases.

Answer 2

ɢɪᴠᴇɴ :-

• Two parallel sides = 21 cm and 9 cm
• Height (h) = 10 cm

ᴛᴏ ғɪɴᴅ :-

• Area of Trapezium

sᴏʟᴜᴛɪᴏɴ :-

We know that,

• Area of Trapezium = ½ × (sum of parallel sides) × (distance between them)

➥ Area = ½ × (21 + 9) × (10)

➥ ½ × 30 × 10

➥ 300/2

➥ 150 cm²

Hence,

• Area of Trapezium = 150 cm²

Therefore,

• Option (c) 150 cm² is correct