Question

How can I find the area of this?

Answer 1

A^2+B^2=C^2
160^2+120^2=c^2
25600+14400=c^2
40000=C^2
square root(40000=c^2)
diagonal is 200m

100^2+b^2=200^2
10000+b^2=40000
b^2=30000
square root(b^2=30000)
Unknown side is 173.2m

120×160×.5= 9600 m^2
this is bottom triangles area

100×173.2×.5=8650 m^2
this is the top triangle area

8650+9600= 18,250 m^2
total area

Answer 2

Find the area of each triangle and then add them together.

Bottom Triangle

A = $\frac{1}{2}$b * h

  = $\frac{1}{2}$(160)(120)

  = 80(120)

  = 9600 m²

Top Triangle

First we need to find the side length. We can calculate the length of the hypotenuse using Pythagorean Theorem for the bottom triangle.

a² + b² = c²

120² + 160² = c²

14400 + 25600 = c²

40000 = c²

200 = c

Now we can use Pythagorean Theorem on the top triangle to find the missing side length.

a² + b² = c²

100² + b² = 200²

10000 + b² = 40000

              b² = 30000

              b ≈ 173

A = $\frac{1}{2}$b * h

  = $\frac{1}{2}$(100)(173)

  = 50(173)

  = 8650 m²

Top Triangle + Bottom Triangle = Total Area

     8650       +        9600

                   18250

Answer: Area = 18,250 m²