Math, asked by jadearmy101, 3 months ago

Step by step answer of the attached picture is appreciated :)

Attachments:

Answers

Answered by sia1234567
38

Answer:

\sf \: first \: divide \: this \: quadrilateral \: into \: 2 \: parts -  \\ \sf after \: dividing \: it \: we \: can \: see \: 2 \: \triangle \: es \\   \bold{\star \:  \triangle \: ABC }\:  \\  \bold{ \star \:  \triangle \: ADC \: }

 \sf \: in \:  \triangle \: ABC\: third \: side \: is \: unknown \:  \\ \sf so \: we \: will \: find \: it  \: out \:out \: through \: pythagoras \: theorem

 \underline{ \underline \bold{ \leadsto \: (hypotnuse)^{2}  = (perpendicular)^{2}  + (base)^{2}}}

 \sf \longmapsto \: ( {hypotenuse})^{2}  =  {9}^{2}  +  {40}^{2}  \\  \sf \longmapsto \:  ({hypotenuse})^{2}  =  \sqrt{1681} \\  {\longmapsto \:   \underline{\fbox{hypotenuse = 41 }}}

 \therefore \: AC = 41

 \sf  \: now \: \: in \:  \triangle \: ABC\: we \: have \: all \: 3 \: sides \\  \sf \: so \: we \: will \: use \: the \: formulae \: of  \: area \: of\: triangle \:

   \underline{\underline\bold{area \: of \:  \triangle \:  =  \frac{1}{2}  \times base \times height}}

 =  \frac{1}{2}  \times 9 \times 40 \\  = 180 \: m^{2}

 \sf \hookrightarrow \: so \: area \: of \:  \triangle \: ABC \:    \bold\red{=  {180 \: m}^{2} }

  \sf\dagger \: now \: for \: finding \: the \: area \: of \: other \:  \triangle \: we \: will \: use \: herons \: formulae

 \underline{ \underline\bold{\leadsto \: semiperimeter =  \frac{a + b + c}{2} }}

 \longmapsto \sf \: semiperimeter \:  =  \frac{41 + 28 + 15}{2}  = 42

 \underline{ \underline \bold{ \bigstar \: area =  \sqrt{s(s - a)(s - b)(s - c)} }}

 \sf \: area =  \sqrt{42(42 - 41)(42 - 28)(42 - 15)}

 \sf \mapsto \: area =  \sqrt{42 \times 1 \times 14 \times 27}

 \sf \mapsto \: area =  \sqrt{15876}

 \sf \longmapsto \: area = 126

 \hookrightarrow \sf \: so \: area \: of \triangle \: ADC \bold \red{ = 126 \: m^{2}}

 \sf \: now \: add \: both \:  \triangle \: es \: area \: to \: get \: total \: area \: of \: quadrilateral \:

 \underline \bold{ \leadsto \: 180 + 126 =  \pink{306 \: m ^{2}}}

________________________________

Similar questions