Question

The sides of triangle ABC are 4.5feet 7.5 ft and 9 ft.The area is about 17 square feet. Explain how to use the are of triangle ABC to find the area of a triangle DEF with side lengths of 6 ft 10 ft and 12ft.Thank you

Answer 1

Area of DEF = 30.22 square feet

Explanation:

Let us find the ratio of sides of the triangles

`(6)/(4.5)=(4)/(3)`

`(10)/(7.5)=(4)/(3)`

`(12)/(9)=(4)/(3)`

So DEF is a similar triangle to ABC with proportion
`(4)/(3)`

If the sides are in a proportion m their areas are in proportion m²

Area of DEF
`=\left ( (4)/(3) \right )^2*` Area of ABC

Area of DEF
`=\left ( (4)/(3) \right )^2* 17`

Area of DEF = 30.22ft²

Answer 2

In order to get the area of a triangle using sides, the formula that we are going to use is Heron's formula. This is after from "Hero of Alexandria".
So here is the step by step process:
First, we calculate for s (half of the triangles perimeter) s = a+b+c divided by 2.
s = 6 + 10 + 12 / 2
s =28/2
s = 14
Now that we have the s, we can now calculate for the area.
A = square root of s(s-a)(s-b)(s-c)
A= square root of 14 x 8 x 4 x 2
A= square root of 896
A = 29.93
The area of triangle DEF is 29.93 square feet or 30 square feet. Hope this answer helps.