Question

two prallel sides of a trapazium are 60m and 77m, and the nonparallel sides are 25m and 26m. find the area of the trapazium.​

Answer 1

$\pink{\mathrm{ \: Two \: parallel \: sides \: = 60m \: \: and \: \: 77m}} \\ \purple{\mathrm{Two \: non \: parallel \: sides = 25m \: and \: 26m}} \\ \\ \blue{\boxed {\mathrm{construction: draw \: a \: perpendicular \: CF}}}\\ \\ \\ \pink {\mathrm{AD-AE=ED}}\\ \\ \rightarrow \mathrm {ED=77-60m }\\ \\ \rightarrow\purple {\boxed {\mathrm {ED= 17m}}} \\ \\ \\ \\ \tiny \bf by using herons formula in △CED \\ \\ \sf a=25m, b= 26m , c=17m \\ \\ \rightarrow \sf \pink {semi perimeter (s)= \frac {a+b+c}{2}=\frac {25+26+17}{2}= \frac {68}{2}}\\ \sf\rightarrow\pink{\boxed{s=34m}}\\ \\ \\ \sf Area of △CED= \sqrt{s(s-a)(s-b)(s-c)}\\ \\ \sf =√34(34 - 25)(34 - 26)(34 - 17) \\ \ sf = √34×9×8×17 \\ \sf = √2×17×3×3×2×2×2×17\\ \sf = 2×2×3×17 \\ \sf Area = 204 m^2 \\ \\ \\ \\ \bf Area of triangle CED =\frac{1}{2}×Base×height\\ \sf 204=\frac {1}{2}×17×height \\ \sf 204 ×\frac {2}{17}=height \\ \rightarrow \sf\purple{\boxed{height=24m}}\\ \\ \\ \bf Now, area of trapezium :- \\ \\ \\ \sf Area of trapezium = \frac {1}{2}×(sum of || lines)×height \\ \\ \sf =\frac {1}{2} ×(60+77)×24\\ \\ \sf =\frac {1}{2}×137×24 \\ \\ \sf = 137×12 \\ \\ \bf \purple {Area=1644 m^2}$

Therefore, area of trapezium is 1644 m^2.

HOPE IT HELPS YOU DEAR.. ^-^