Question

Triangle XYZ, with vertices C(-8,4), Y(-4,3-), and Z(-5,6), is drawn inside a rectangle. What is the area, in square units, of triangle XYZ?

Answer 1

Approx. 5.5 sq units.

Explanation:

Here is how you do it:

To find the area of triangle XYZ, we can use the formula for the area of a triangle given its vertices in the coordinate plane.

Given the vertices of triangle XYZ:

C (-8, 4)

Y (-4, 3)

Z (-5, 6)

To find the area of the triangle, we can use the Shoelace Formula. The formula is as follows:

Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|

Substituting the coordinates into the formula, we get:

Area = 1/2 * |((-83) + (-46) + (-54)) - ((4(-4)) + (3*(-5)) + (6*(-8)))|

= 1/2 * |(-24 - 24 - 20) - (-16 - 15 - 48)|

= 1/2 * |-68 - (-79)|

= 1/2 * |-68 + 79|

= 1/2 * |11|

= 1/2 * 11

= 11/2

Therefore, the area of triangle XYZ is 11/2 square units, which is equal to 5.5 square units

Here is an alternate method:

Call the rectangle as A(-8,6), B(-4,6), C(-4,3), D(-8,3)

THen,

Area of XAZ : 1/2 *3*2 = 3

Area of ZBY : 1/2 *1*3 = 1.5;

Area of XDY : 1/2 * 1 * 4 = 2

Area of rect: 3*4 = 12;

Finally area of the given triangle XYZ = 12-3-1.5-2
= 5.5 Sq units.