Question

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

Answer 1

Answer:

37.5 square units

Step-by-step 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

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

$AB = \sqrt{12^2 + 9^2}$

$AB = \sqrt{144 + 81}$

$AB = \sqrt{225} = 15$

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

$CD = \sqrt{(3)^2 + (-4)^2}$

$CD = \sqrt{9 + 16}$

$CD = \sqrt{25} = 5$

✍️Area of a ∆ABC =½*AB*CD

= ½*15*5

✅ Area = 37.5 square units