Question

The lengths of the shorter and longer parallel sides of a trapezium are a and b cm respectively. If the area of the trapezium is 4 ( a^2 - b^2 ) , then the height of the trapezium is

guys please tell me the height of trapezium and the correct answer is 8 ( a - b) , please don't scam or i will report you. Please tell its answer it is urgent.
​

Answer 1

Step-by-step explanation:

1/2(a+b)h= 4(a^2-b^2)

(a+b)h= 4*2(a-b)(a+b)

h=8(a-b)(a+b)-(a+b)

h=8(a-b)

height =8(a-b) solved

Answer 2

$\boxed{ \red{AnswEr:-}}$

• 8( a - b )

★ GivEn :-

• The lengths of the shorter and longer parallel sides of a trapezium are a and b cm respectively.
• The area of the trapezium is 4 (a² - b²) cm².

★ To Find :-

• The height of trapezium

★ Diagram :-

• Refer to the attachment.

$\boxed{ \red{Solution:-}}$

➠ Firstly, let's know the formula of area of trapezium.

$\implies \boxed{ \sf{ \bold{ \red{A = \dfrac{a + b}{2} \times h}}}}$

Where,

• A = Area of trapezium
• a = Length of shorter parallel side
• b = Length of longer parallel side
• h = Height of the trapezium

➠ In the question, area of trapezium is given. So we will put the value there and find the length of height.

$\implies \sf \: \dfrac{a + b}{2} \times h = 4( {a}^{2} + {b}^{2} )$

$\implies \sf \: \dfrac{a + b}{2} \times h = 4(a + b)(a - b)$

$\implies \sf \: h = 4(a + b)(a - b) \times \dfrac{2}{(a + b)}$

$\implies \sf \: h = 4(a - b) \times 2$

$\implies \boxed{ \sf{ \red{ \bold{h = 8(a - b)}}}}$