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

`Area = 112.5`

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 = |(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 = |(15(5 -5) + 15(20 - 5) + 0(20 - 5))/(2)|`

`Area = |(15(0) + 15(15) + 0(15))/(2)|`

`Area = |(0 + 225 + 0)/(2)|`

`Area = |(225)/(2)|`

`Area = |112.5|`

`Area = 112.5`

Hence, the area of the triangle is 112.5