Question

find the area of a trapezium where it's 2 unequal sides are parallel and dimensions are 26 cm,13 cm,16 cm,13 cm

Answer 1

Given:

$\bigstar \bold{\green{\texttt{Dimensions of a Trapezium = 26cm, 13cm, 16cm and 13cm}}}$

$\bigstar \bold{\green{\texttt{It's two unequal sides are parallel}}}$

To Find : The Area of trapezium

Construction: Construct a parallel line to AB from point C to point E on AD, such that BC = AE, AB = CE and AB || CE

$\therefore \sf AE = BC = \bold{16cm} \\ \therefore \sf ED = AD - AE = 26cm - 16cm = \bf 10cm$

${\boxed{\bold{\green{\texttt{Using, Heron's Formula for Area of Triangle}} = \sqrt{s(s-a)(s-b)(s-c)}}}} \\ \bold{\red{\texttt{Where value of 's'}}= \frac{a+b+c}{2}} \\ \bold{\red{\texttt{a, b, and c are sides of the triangle}}}$

$\therefore \bold{\texttt{In ΔCDE,}} \\ \sf a = 10cm, \\ \sf b = 13cm, \\ \sf c = 13cm$

$\texttt{Value of semi-perimeter, s = \sf \blue{\frac{10+13+13}{2} = \frac{36}{2}} = 18 }$

So, Putting the values in Hereon's Formula :

$\therefore \sf \sqrt{18(18 - 10)(18 - 13)(18 - 13)} \\ \sf \implies \sqrt{18 \times 8 \times 5 \times 5} \\ \sf \implies \sqrt{3600} \\ \sf \implies \bold{\red{60cm^2}}$

We get area of the ΔDCE = $\bold{ 60cm^2 }$

Also :

${\boxed{\bold{\green{\texttt{Using, another Formula for Area of Triangle}} = \frac{1}{2}bh}}} \\ \bold{\red{\texttt{Where b is base and h is height}}}$

Area of ΔDEC = $\sf 60cm^2$

base = 10cm

height = ?

So, Using the formula on ΔDEC again,

$\therefore \sf 60cm^2 = \frac{1}{2} \times 10 \times h \\ \sf \implies 60cm^2 = 5 \times h \\ \sf \implies h = \frac{60cm^2}{5} \\ \sf \implies {\bold{\red{h = 12cm}}}$

Now,

$\boxed{\bold{\green{\texttt{Area of trapezium}}} = \sf \frac{a+b}{2}h}$

$\sf a = 16cm \\ \sf b = 26cm \\ \sf h = 12cm$

Putting the values,

$\therefore \sf A = \frac{16+26}{2} \times 12 \\ \sf \implies \frac{42}{2} \times 12 \\ \sf \implies 21 \times 12 \\ \sf \implies \bold{\red{252cm^2}}$

Hence,

$\bold{\pink{\textrm{Area of the given trapezium is \sf 252cm^2 }}}$

Answer 2

Answer:

Area of the given trapezium is 252cm sq