Question Number 178941 by ARUNG_Brandon_MBU last updated on 23/Oct/22
Commented by HeferH last updated on 23/Oct/22
$${is}\:{AC}={DE}? \\ $$
Commented by Ar Brandon last updated on 23/Oct/22
No. They are given to be parallel.
Answered by som(math1967) last updated on 23/Oct/22
![join AE area △ACD=area△AEC [same base AC, AC∥DE] area△ABC+△ACD=△ABC+△AEC area(ABCD)=area△ABE area(ABCD)=(1/2)×4×7=14cm^2](Q178950.png)
$${join}\:{AE}\: \\ $$$$\:{area}\:\bigtriangleup{ACD}={area}\bigtriangleup{AEC} \\ $$$$\left[{same}\:{base}\:{AC},\:{AC}\parallel{DE}\right] \\ $$$${area}\bigtriangleup{ABC}+\bigtriangleup{ACD}=\bigtriangleup{ABC}+\bigtriangleup{AEC} \\ $$$${area}\left({ABCD}\right)={area}\bigtriangleup{ABE} \\ $$$${area}\left({ABCD}\right)=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{4}×\mathrm{7}=\mathrm{14}{cm}^{\mathrm{2}} \\ $$
Commented by som(math1967) last updated on 23/Oct/22
Commented by Ar Brandon last updated on 23/Oct/22
Thank you Sir
Commented by cortano1 last updated on 23/Oct/22
$$\mathrm{why}\:\mathrm{area}\:\Delta\mathrm{ACD}\:=\:\Delta\:\mathrm{ACE}\:? \\ $$
Commented by MJS_new last updated on 23/Oct/22
$$\mathrm{triangles}\:\mathrm{with}\:\mathrm{same}\:\mathrm{base}\:\mathrm{and}\:\mathrm{same}\:\mathrm{height} \\ $$$$\mathrm{have}\:\mathrm{same}\:\mathrm{area}.\:{AC}\:\mathrm{is}\:\mathrm{the}\:\mathrm{base}\:\mathrm{and}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{parallels}\:\mathrm{is}\:\mathrm{the}\:\mathrm{height} \\ $$
Commented by som(math1967) last updated on 23/Oct/22
$${they}\:{are}\:{in}\:{same}\:{base}\:{AC}\:{and} \\ $$$${between}\:{parallel}\:{AC}\:{and}\:{DE} \\ $$