Question

$:\implies{ \underline{ \boxed {\bf{\red{Answer \: This }}}}}$
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Answer 1

Given :-

• AD ║ BC  
• AD  = 26 cm
• BC = 60 cm
• AC = 61 cm ( diagonal )

To Find :-

• Area of the trapezium ABCD

Solution :-

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

$\sf \mapsto Area\;of\;Trapezium = \dfrac{(a+b)h}{2}$

Where ,

a and b are the parallel sides ( AD and BC )

h is the height  ( AB )

→ In this Trapezium AB is the height whose value is not given to us . We can see that  Δ ABC is a right angled - triangle and we can apply the pythagoras theorm to find the height

→ According to the pythagorean theorm in Δ ABC

AB ²  + BC ²  = AC ²

→ Let's solve by putting the values

⇒  AB² + 60² = 61²

⇒ AB² + 3600 = 3721

⇒ AB²  = 3721 - 3600

⇒ AB² = 121

⇒ AB = √121

⇒ AB = 11

→ ATQ , we need to find the area of the trapezium . let's find out

$\sf \leadsto \dfrac{(26+60) \times 11 }{2}$

$\sf \leadsto \dfrac{86 \times 11}{2}$

$\sf \leadsto 43 \times 11$

$\sf \leadsto 473 \; cm^{2}$

∴ Area of the Trapezium is 473 cm²  ( Option a )