Question

Find the height of the trapezium whose parallel sides and area are 14cm, 16cm and150 cm2

respectively​

Answer 1

Given :

• Area of Trapezium = 150cm²
• First Parallel Side = 14cm
• Second Parallel Side = 16cm

To Find :

• Height of Trapezium

Solution :

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

⠀

⟹ Area of Trapezium = ½ × h × (S1 + S2)

⟹ 150 = ½ × h × (14 + 16)

⟹ 150 × 2 = h × (14 + 16)

⟹ 300 = h × (14 + 16)

⟹ 300 = h × 30

⟹ 300/30 = h

⟹ 10cm = height

________________

Verification :

➟ Area of Trapezium = ½ × h × (S1 + S2)

➟ Area of Trapezium = ½ × 10 × (14 + 16)

➟ Area of Trapezium = ½ × 10 × 30

➟ Area of Trapezium = 5 × 30

➟ 150 = 150

Hence Verified

________________

Therefore :

• Height of Trapezium is 10cm

________________

Answer 2

Correct Question :-

Find the height of the trapezium whose parallel sides and area are 14cm, 16cm and 150 cm² respectively.

Given :-

First parallel side = 14cm

Second parallel side = 16cm

Area of trapezium = 150cm²

To find :-

Height of trapezium.

Using formula :-

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

Solution:-

First parallel side = 14cm

Second parallel side = 16cm

Height = ?

Area of trapezium = 150cm²

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

$\sf 150cm^2= \dfrac{1}{2} \times height \times (14cm+16cm)$

$\sf 150cm^2\times 2= height \times (14cm+16cm)$

$\sf 300cm^2 = height \times 30cm$

$\sf height = \dfrac{300cm^2}{30cm}$

$\sf height =\cancel \dfrac{300cm^2}{30cm}$

$\sf height = 10cm$

Therefore,

Height of trapezium = 10cm