Question

Find the area of the triangle with the given vertices.
A(4,2), B(2,-2), C(-2,5)

Answer 1

15 units²

Explanation:

ΔABC is a right triangle with:

• AB = shortest leg
• AC = longest leg
• BC = hypotenuse
• ∠BAC = 90°

Area of a triangle = 1/2 x base x height

⇒ area = 1/2 x AB x AC

Use the distance formula to find the lengths:

`\sf distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

(where
`\sf (x_1,y_1) \ and \ (x_2,y_2)` are the endpoints)

`\sf AB=√((2-4)^2+(-2-2)^2)=2√(5)`

`\sf AC=√((-2-4)^2+(5-2)^2)=3 √(5)`

`\sf \implies area=\frac12 * 2√(5) * 3√(5) =15 \ units^2`