Question

The area of a trapezium is 34 cm² and the length of one of the parallel sides is
10 cm and its height is 4 cm. Find the length of the other parallel side.​

Answer 1

Answer:

other parallel side lenght=7 cm

Step-by-step explanation:

area of trapezium(34 cm^2)=1/2×(sum of parallel sides)×height(4 cm)

then let a be other parallel side length

34=1/2×(10+a)×4

a=7cm

Answer 2

Given Information :

• Area of the trapezium → 34 cm²
• The length of the parallel sides → 10 cm
• Height of the trapezium → 4 cm

What we have to do ?

We will consider the Unknown length of the other parallel side be in terms of variable and then we will apply the formula for calculating the area of the trapezium. Simply substituting the values and then we got our length.

Formula need to know :

$\boxed{\bf{Area \: of \: Trapezium = \dfrac{1}{2} ( Sum \: of \: parallel \: sides) \times h}}$

Now,

Let us we consider the length be " l " cm

Applying the formula, we get

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

$\bigstar\:\underline{\textbf{As per the Question :}}$

Substituting the respective values, we get :

$\dashrightarrow\:\:\sf 34 = \dfrac{1}{2} \times (10 + l) \times 4$

$\sf \longrightarrow \: 34 \: = {\dfrac{1}{ \cancel{2}^{ \: \: 1} } \: (10 + l) \: \cancel{4}^{ \: \: 2} \: cm}$

$\dashrightarrow\:\:\sf 34 = (10 + l) \times 2$

$\dashrightarrow\:\:\sf 34 = 20 + 2l$

$\dashrightarrow\:\:\sf 34 - 20 = 2l$

$\dashrightarrow\:\:\sf 14 = 2l$

$\sf \longrightarrow \: l \: = {\dfrac{ \cancel{14}^{ \: \: 7} }{ \cancel{2}^{ \: \: 1} } \: cm}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Other \: length \: of \: Trapezium = 7 \: cm}}$

Not sure about the answer ?

Lets verify to confirm -

For Verification :

$:\implies \sf 34 = \dfrac{1}{2} (Sum \: of \: sides) \times h$

$:\implies \sf 34 = \dfrac{1}{2} \times (10 + 7) \times 4$

$\sf \longrightarrow \: 34 \: = {\dfrac{1}{ \cancel{2}^{ \: \: 1} } \: (10 + 7) \: \cancel{4}^{ \: \: 2} \: cm}$

$:\implies \sf 34 = (10 + 7) \times 2$

$:\implies \sf 34 = 17 \times 2$

$:\implies \sf 34 = 34$

$:\implies \bf LHS = RHS$

$\underline{\sf Verified ! }$