Question

You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area a of the shelf X is (15,20) Z is (0,5) Y is (15,5)

Answer 1

Answer:

$Area = 112.5$

Step-by-step explanation:

Given

$X = (15,20)$

$Y = (15,5)$

$Z = (0,5)$

Required

Determine the area of the triangle

The area is calculated using the following formula:

$Area = |\frac{X_x(Y_y - Z_y) + Y_x(X_y - Z_y) + Z_x(X_y - Y_y)}{2}|$

Where

$(X_x,X_y) = (15,20)$

$(Y_x,Y_y) = (15,5)$

$(Z_x,Z_y)= (0,5)$

Substitute right values in the given formula:

$Area = |\frac{15(5 -5) + 15(20 - 5) + 0(20 - 5)}{2}|$

$Area = |\frac{15(0) + 15(15) + 0(15)}{2}|$

$Area = |\frac{0 + 225 + 0}{2}|$

$Area = |\frac{225}{2}|$

$Area = |112.5|$

$Area = 112.5$

Hence, the area of the triangle is 112.5