Question

What is the area of this triangle ?

Answer 1

Area of triangle is 9.88 units^2

Explanation:

We need to find the area of triangle

Given E(5,1), F(0,4), D(0,8)

We will use formula:

`Area\,\,of\,\,triangle =√(s(s-a)(s-b)s-c)) \\where\,\, s = (a+b+c)/(2)`

We need to find the lengths of side DE, EF and FD

Length of side DE = a =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Length of side DE = a =
`=√((5-0)^2+(1-8)^2)\\=√((5)^2+(-7)^2)\\=√(25+49)\\=√(74)\\=8.60`

Length of side EF = b =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Length of side EF = b =
`=√((0-5)^2+(4-1)^2)\\=√((-5)^2+(3)^2)\\=√(25+9)\\=√(34)\\=5.8`

Length of side FD = c =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Length of side FD = c =
`=√((0-0)^2+(8-4)^2)\\=√((0)^2+(4)^2)\\=√(0+16)\\=√(16)\\=4`

so, a= 8.60, b= 5.8 and c = 4

s = a+b+c/2

s= 8.6+5.8+4/2

s= 9.2

Area of triangle=
`=√(s(s-a)(s-b)s-c))\\=√(9.2(9.2-8.6)(9.2-5.8)(9.2-4))\\=√(9.2(0.6)(3.4)(5.2))\\=√(97.5936)\\=9.88`

So, area of triangle is 9.88 units^2