Question

I have no idea!! Please help!!!

Answer 1

The area of a traingle is
`(1)/(2)bh`
So we need to know the base and the height
To work out the sides of a right angle triangle we can use a²+b²=c
c is the hypotenuse and a and b are the other sides
Because this triangle is isoceles we know that a and b are the same

a²+b²=c²
a²+a²=c²
2a²=c²
2a²=(x√6)²
2a²=(x√6)(x√6)
2a²=x²+x√6+x√6+6
2a²=x²+x√6+x√6+6
a²=
`(x^(2)+x √(6)+x √(6)+6 )/(2)`
a=
`\sqrt{(x^(2)+x√(6)+x√(6)+6)/(2)}`

A=
`(1)/(2)bh`
A=
`(1)/(2)a*a`
A=
`(1)/(2)`×
`\sqrt{(x^(2)+x√(6)+x√(6)+6)/(2)}`×
`\sqrt{(x^(2)+x√(6)+x√(6)+6)/(2)}`
A=
`(1)/(2)`×
`(x^(2)+x √(6)+x √(6)+6 )/(2)`
A=
`(x^(2)+x √(6)+x √(6)+6 )/(4)`