Question

Parallel sides of trapezium are 60 and 77. Other sides are 25 and 26. Find the area.

Answer 1

Hint: In this question first we have to draw the diagram and then measure the side. For solving this question, we have to know the formula of the area of trapezium which is $\dfrac{1}{2}$(sum of parallel side). height
First, we have to find the height of the trapezium

Complete step-by-step answer:
First draw the diagram,

We have two parallel side AD = 60 and BC = 77
And two other side is AB = 25 and DC = 26
When we join AE and DF we find that both lines are perpendicular on BC
And angle E and angle F is right angled
Now AE and DF are the height of the trapezium
First, we have to find the length of height
Let BE is x
Then in right angle triangle AEB
$A{B^2} = A{E^2} + B{E^2} $
Putting the values
$ \Rightarrow$${25^2} = A{E^2} + {x^2} $
Now in right angle triangle DFC
$D{C^2} = D{F^2} + F{C^2} $.........……………..(1)
Here BC = BE + EF + FC
$ \Rightarrow$$77 = x + 60 + FC$
Here FC = $17 - x$
Now putting the values in (1)
$ \Rightarrow$${26^2} = D{F^2} + {(17 - x)^2}$
Height of the trapezium are equal, so we have
$A{E^2} = D{F^2} $
$ \Rightarrow$${25^2} - {x^2} = {26^2} - {(17 - x)^2}$
$ \Rightarrow$$625 - {x^2} = 676 - (289 + {x^2} - 34x) $
$ \Rightarrow$$625 - {x^2} = 676 - 289 - {x^2} + 34x$
Taking the variable and consent
$ \Rightarrow$$625 - {x^2} = 387 - {x^2} + 34x$
$ \Rightarrow$$ - {x^2} + {x^2} - 34x = 387 - 625$
$ \Rightarrow$$ - 34x = - 238$
$ \Rightarrow$\[x = \dfrac{{ - 238}}{{ - 34}}\]
Dividing the numerator by denominator
$x = 7$
So now we can find the height
$A{B^2} = A{E^2} + B{E^2} $
$ \Rightarrow$${25^2} = A{E^2} + {x^2} $
Putting the value of $x = 7$
$ \Rightarrow$${25^2} = A{E^2} + {7^2} $
$ \Rightarrow$$625 - 49 = A{E^2} $
$ \Rightarrow$$AE = \sqrt {576} $
$ \Rightarrow$$AE = 24$
Now we have the height of the trapezium we can find the area
Area of trapezium =$\dfrac{1}{2}$(sum of parallel side). height
Putting the values, we get
$ = \dfrac{1}{2}(60 + 77).24$
$ = \dfrac{1}{2}137.24$
$ = \dfrac{{3288}}{2}$
$ = 1644$$c{m^2} $

The area of trapezium is $1644$$c{m^2} $

Note: Pythagoras theorem states that the sum of squares of base and adjacent is equal to the square of the hypotenuse.
$(A^2) + (O^2) = (H^2)$