Question

Which statement best describes the area of Triangle ABC shown below? A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 4, vertex B is on ordered pair 7 and 2, and the vertex C is on ordered pair 1 and 2. (5 points) a It is one-half the area of a square of side length 6 units. b It is twice the area of a square of side length 6 units. c It is one-half the area of a rectangle with sides 6 units × 2 units. d It is twice the area of a rectangle with sides 6 units × width 2 units.

Answer 1

c.

Explanation:

I go a slightly different route than the other answer.

let's see the side lengths of the triangle :

AB² = (7-4)² + (2-4)² = 3² + (-2)² = 9 + 4 = 13

AB = sqrt(13)

BC² = (1-7)² + (2-2)² = (-6)² + 0² = 36

BC = 6

CA² = (4-1)² + (4-2)² = 3² + 2² = 9 + 4 = 13

CA = sqrt(13)

it is an isoceles triangle (the legs have the same length).

so, we get the height via Pythagoras (for the right-angled triangle with height and BC/2 as legs) :

CA² = height² + (BC/2)²

13 = height² + 3² = height² + 9

height² = 4

height = 2

and the area of the triangle is then (baseline×height/2) :

6×2 / 2

and that is half of the area of a 6×2 rectangle.