# If D , E (7 , 3) and F are the mid-points of the sides of triangle ABC , then find the area of the triangle ABC.

2
by SweetRohan

tomorrow i will do

pls do it now

no time sorry

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by SweetRohan

tomorrow i will do

pls do it now

no time sorry

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

First to find the area we need to find the vertices of the triangle.

Midpoint D = x1+x2 = -1........(1)

y1+y2 = 5.............................(4)

Midpoint E = x1+x3 = 14.........(2)

y1+y3 = 6...............................(5)

Midpoint F = x2+x3 = 7............(3)

y2+y3 = 7...............................(6)

Now let us find the x terms first.

(1) ........ x1 = -1-x2

Sub in (2) ........ -1-x2 + x3 = 14........(7)

Now subtracting (7) and (3)

we get, 2x3 = 22

**x3 = 11**

Sub x3 in (2) ........x1+11 = 14

**x1 = 3**

and so**x2 = -4**

now let us find y terms.

(3) ............y1 = 5 - y2

sub in (5).........5-y2+y3 = 6.........(8)

Now subtracting (8) and (6) we get,

**y3 = 4**

now sub y3 in (5)......**y1 = 2**

and so

**y2 = 3**

**now the vertices are (3,2) (-4,3) (11,4)**

**Area of the triangle **= (3(3-4) + (-4) (4-2) + 11(2-3))/2

= (-3 -8 -11)2

= - 11

Remove the negative sign (-) from the number -11.

**The area of the triangle is 11 sq.units.**

Because the formula calls for absolute value, you simply remove the negative sign.

Midpoint D = x1+x2 = -1........(1)

y1+y2 = 5.............................(4)

Midpoint E = x1+x3 = 14.........(2)

y1+y3 = 6...............................(5)

Midpoint F = x2+x3 = 7............(3)

y2+y3 = 7...............................(6)

Now let us find the x terms first.

(1) ........ x1 = -1-x2

Sub in (2) ........ -1-x2 + x3 = 14........(7)

Now subtracting (7) and (3)

we get, 2x3 = 22

Sub x3 in (2) ........x1+11 = 14

and so

now let us find y terms.

(3) ............y1 = 5 - y2

sub in (5).........5-y2+y3 = 6.........(8)

Now subtracting (8) and (6) we get,

now sub y3 in (5)......

and so

= (-3 -8 -11)2

= - 11

Remove the negative sign (-) from the number -11.

Because the formula calls for absolute value, you simply remove the negative sign.

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

If DEF is the triangle formed by joining the mid-points of sides of the triangle ABC, then the area of triangle ABC is 4 times the area of triangle DEF.

So find the area of triangle DEF first and multiply with 4 to get the area of ABC.

Area of a triangle with vertices (x₁,y₁); (x₂,y₂) and (x₃,y₃) is given by

Area = [ x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) ] / 2

Vertices of DEF are

So Area of triangle DEF

So area of DEF is

So area of ABC =

So find the area of triangle DEF first and multiply with 4 to get the area of ABC.

Area of a triangle with vertices (x₁,y₁); (x₂,y₂) and (x₃,y₃) is given by

Area = [ x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) ] / 2

Vertices of DEF are

So Area of triangle DEF

So area of DEF is

So area of ABC =