If D-15- 52- E7- 3 and F72- 72 are the mid-points of sides of - ABC- find the area of - ABC-

Area of ABC=4× Area of DEF = gt; Area of #160; ABC=4× 1 2 7 2 #160; amp; 7 2 #160; 7 amp; 3 1 5 #160; am ...

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Byju's Answer

Standard VIII

Mathematics

Area of Polygons

If D-15, 52...

Question

If $D (- \frac{1}{5}, \frac{5}{2}), E (7, 3)$ and $F (\frac{7}{2}, \frac{7}{2})$ are the mid-points of sides of $Δ A B C$ , find the area of $Δ A B C$ .

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Solution

Area of $△ A B C = 4 \times$ Area of $△ D E F$
=> $A r e a o f △ A B C = 4 \times \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{7}{2} & \frac{7}{2} 7 & 3 - \frac{1}{5} & \frac{5}{2} \frac{7}{2} & \frac{7}{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ = 4 \times \frac{1}{2} | \frac{21}{2} - \frac{49}{2} + \frac{35}{2} + \frac{3}{5} - \frac{7}{10} - \frac{35}{4} | = 2 (107) = 214$

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Q. Question 16
If D

(\frac{- 1}{2}, \frac{5}{2})

, E (7,3) and F

(\frac{7}{2}, \frac{7}{2})

are the mid-points of sides of

Δ A B C

, then find the area of the

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If D $(\frac{- 1}{5}, \frac{5}{2})$ , E (7, 3) and F $\frac{7}{2}, \frac{7}{2}$ are the mid points of sides of $△ A B C$ , find the area of $△ A B C$ .

Q. If

D (- \frac{1}{5}, \frac{5}{2}), E (7, 3) and F (\frac{7}{2}, \frac{7}{2})

are the mid-points of sides of

∆ A B C

, find the area of

∆ A B C

Q. Question 16
If D

(\frac{- 1}{2}, \frac{5}{2})

, E (7,3) and F

(\frac{7}{2}, \frac{7}{2})

are the mid-points of sides of

Δ A B C

, then find the area of the

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If D(−15,52),E(7,3) and F(72,72) are the mid-points of sides of ΔABC, find the area of ΔABC.

Area of △ABC=4×Area of △DEF=>Areaof△ABC=4×12∣∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣∣727273−15527272∣∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣∣=4×12|212−492+352+35−710−354|=2(107)=214

If $D (- \frac{1}{5}, \frac{5}{2}), E (7, 3)$ and $F (\frac{7}{2}, \frac{7}{2})$ are the mid-points of sides of $Δ A B C$ , find the area of $Δ A B C$ .