To find the area, you have to split the triangle into two right triangles.
Then, use the Pythagorean Theorem to find the missing side length on the bottom.
For the left triangle,
[tex] a^{2} + b^{2} = c^{2} [/tex]
[tex]1.8^{2} + b^{2} = 3.3^{2}, b = bottom side[/tex]
[tex]3.24 * b^{2} = 10.89[/tex]
[tex]b = 2.756[/tex]
For the right triangle,
[tex] a^{2} + b^{2} = c^{2} [/tex]
[tex]1.8^{2} + b^{2} = 2.2^{2}, b = bottom side[/tex]
[tex]3.24 * b^{2} = 4.84[/tex]
[tex]b = 1.265[/tex]
Using these, we can determine area of both triangles and add them together to get the total area of the triangle.
Left triangle's area =
[tex] \frac{1}{2} * base * height[/tex]
[tex] \frac{1}{2} * 2.756 * 1.8 = 2.489 ft^{2}[/tex]
Right triangle's area =
[tex] \frac{1}{2} * base * height[/tex]
[tex] \frac{1}{2} * 1.265 * 1.8 = 1.138 ft^{2}[/tex]
Total area =
Left + Right = 3.627 ft^2
To get perimeter, just add all of the original side lengths, except height, together.
3.3 ft + 2.2 ft + 4ft = 9.5 ft
Hope this helps!
