Question

The area of a trapezium in 540msquare. Two of its parallel sides are 40m and 32m. Find the distance between the two parallel sides.​

Answer 1

Given:

• The area of a trapezium in 540m².

• Two of its parallel sides are 40m and 32m.

To calculate:

• The distance between the two parallel sides i.e height of the parallelogram.

Calculation:

As we know that,

$\star$ $\boxed{\sf \pink { {Area}_{(Trapezium)} = \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times h }}$

But, according to the question :

$\sf { \longrightarrow 540 \: {m}^{2} = \dfrac{1}{2} \times (40 + 32) \times h \: {m}^{2} }$

$\sf { \longrightarrow 540 \: {m}^{2} = \dfrac{1}{2} \times (72) \times h \: {m}^{2} }$

$\sf { \longrightarrow 540 \: {m}^{2} = 1 \times 36 \times h \: {m}^{2} }$

$\sf { \longrightarrow 540 \: {m}^{2} = (36 \times h) \: {m}^{2} }$

$\sf { \longrightarrow \dfrac{540 \: {m}^{2} }{36 \: m} = h \: m }$

$\longrightarrow$ $\boxed{\sf { h \: m = 15 \: m }}$

Therefore, distance between the two parallel sides or height of the trapezium is 15 m.

Verification:

$\star$ $\boxed{\sf \pink { {Area}_{(Trapezium)} = \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times h }}$

Here,

• LHS= Area of the trapezium

→ LHS= 540m²

• RHS = $\sf{ \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times h }$

→ $\sf { RHS= \dfrac{1}{2} \times (40+2) \times 15 \: {m}^{2} }$

→ $\sf { RHS= \dfrac{1}{2} \times 72 \times 15 \: {m}^{2} }$

→ $\sf { RHS= 36 \times 15 \: {m}^{2} }$

→ $\sf { RHS= 540 \: {m}^{2} }$

Hence,

$\longrightarrow$ $\boxed{\sf { LHS = RHS }}$

$\longrightarrow$ $\boxed{\sf { 540 \: {m}^{2} = 540 \: {m}^{2} }}$

Hence, verified!!

More to know :

• Trapezium

• It has 4 sides.
• It has a pair of parallel sides.

$\star$ $\boxed{\sf \pink { {Area}_{(Trapezium)} = \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times h }}$

$\star$ $\boxed{\sf \pink { {Perimeter}_{(Trapezium)} = Sum \: of \: all \: sides }}$

Answer 2

Answer:

Step-by-step explanation:

Area of the trapezium = 540 m^2

Parallel sides of the trapezium = 14 m and 32 m.

Let distance between of the two parallel sides be h m.

We know that

Area of trapezium = 1/2 × ( sum of // sides ) × h

=> 540 = 1/2 × ( 14 + 32 ) × h

=> 540 = 1/2 × 46 × h

=> 540 = 23 × h

=> h = 540 / 23

=> h = 23.4 m

Hence, distance between of the two parallel sides is 23.4 m