Question

ABC is a triangle in which D is the midpoint of B.C..E and F are mid points of D.C. and AE respectively.if area of triangle abc is 16 cm square,find the area of triangle def.

Answer 1

Aиѕωєr —

Area of ∆DEF = 2 cm²

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Cσrrєcт Qυєѕтiσи —

ABC is a triangle in which D is the midpoint of BC .E and F are mid points of DC and AE respectively .If area of ∆ABC is 16 cm² , find the area of ∆DEF.

Giνєи —

• ABC is a triangle
• D is the midpoint of BC
• E is the midpoint of CD
• F is the midpoint of A
• Area of ∆ABC = 16 cm²

Tσ Fiиd —

Area of triangle DEF

Sσℓυтiσи –

We know that , median divides a triangle in two triangles of equal areas,

➨For ∆ABC , AD is the median ,

Area of ∆ADC :

$\qquad\rm{\implies \dfrac{1}{2}(area\:of\:\triangle ABC)}$

$\qquad\rm{\implies \dfrac{1}{2}(16)}$

$\qquad\rm{\implies\cancel{\dfrac{16}{2}}}$

$\qquad\rm{\implies 8\:cm^2}$

➨For∆ADC , AE is the median ,

Area of ∆AED :

$\qquad\rm{\implies \dfrac{1}{2}(area\:of\:\triangle ADC)}$

$\qquad\rm{\implies \dfrac{1}{2}(8)}$

$\qquad\rm{\implies\cancel{\dfrac{8}{2}}}$

$\qquad\rm{\implies 4\:cm^2}$

➨Similarly , For ∆AED , DF is the median ,

Area of ∆DEF :

$\qquad\rm{\implies \dfrac{1}{2}(area\:of\:\triangle AED)}$

$\qquad\rm{\implies \dfrac{1}{2}(4)}$

$\qquad\rm{\implies\cancel{\dfrac{4}{2}}}$

$\qquad\rm{\implies 2\:cm^2}$

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Addiтioиαl Iиfσrмαтiσи —

❍ Formulas related to Surface Areas & Volume :

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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$\red{\bigstar}\bf{Note:}$ Kindly view the above formulas in brainly.in website as the latex used in the above formulas is not displayed in the brainly application .

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