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 =
`(1)/(2)`b * h

=
`(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 =
`(1)/(2)`b * h

=
`(1)/(2)`(100)(173)

= 50(173)

= 8650 m²

Top Triangle + Bottom Triangle = Total Area

8650 + 9600

18250

Answer: Area = 18,250 m²