Question

find the area of the trapezium whose parallel sides are 25 and 11 long and the non parrallel sides are 13 and15
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Answer 1

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From the point C construct CE || DA

We know that ADCE is a parallelogram having AE || DC and AD || EC with AD = 13m and D = 11m

AE = DC = 11m and EC = AD = 13m

So we get

BE = AB - AE

BE = 25 -11 = 14m

Consider Δ BCE

We know that BC = 15m, CE = 13m and BE = 14m

Take a = 15m, b = 13m and c = 14m

$\sf \: s = \frac{ a+ b + c}{2} = \frac{15 + 13 + 14}{2} = 21$

s=21cm

We know that

$\sf \: Area = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \frac{21(21 - 15)(21 - 13)(21 - 14)}{2} \\ \\ = \sqrt{21 \times 6 \times 7 \times 8}$

It can be written as

$= \sqrt{7 \times 3 \times 2 \times 3 \times 4 \times 2\times 7}$

We get area= 7×3×2×2

So area= 84 cm²

Area of △ BCE = 1/2×BE×CL

84= 1/2 ×14×CL

84=7×CL

CL=12

We know that

Area of trapezium ABCD = 1/2 × sum of parallel sides × height

Area of trapezium ABCD = 1/2 × (AB + CD) × CL

= 1/2×(11+25)×12

= 36×6=216

So area of trapezium ABCD is 216m²

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