Question

Calculate the area of triangle ABC with altitude, CD, given

A(-6,-4), B(6,5), C(-1,6), and D(2, 2).
Round your answer to the nearest tenth if necessary.
The area of triangle ABC is
square units

Answer 1

37.5 square units

Explanation:

Given:

A(-6,-4), B(6,5), C(-1,6), and D(2, 2), where CD is the altitude if ∆ABC

Required:

Area of ∆ABC

SOLUTION:

Area of a ∆ABC =½*AB*CD

✍️
`AB = √((x_2 - x_1)^2 + (y_2 - y_1)^2) = \sqrt{6 -(-6))^2 + (5 -(-4))^2`

`AB = √(12^2 + 9^2)`

`AB = √(144 + 81)`

`AB = √(225) = 15`

✍️
`CD = √((x_2 - x_1)^2 + (y_2 - y_1)^2) = \sqrt{2 -(-1))^2 + (2 - 6)^2`

`CD = √((3)^2 + (-4)^2)`

`CD = √(9 + 16)`

`CD = √(25) = 5`

✍️Area of a ∆ABC =½*AB*CD

= ½*15*5

✅ Area = 37.5 square units