Question

In a grid of an auditorium, the vertices of a section of seats are A(40, 20) , B(80, 20) , C(100, 70) , and D(40, 70) . The coordinates are measured in feet. Find the area of the section.

Answer 1

`Area = 2900`

Explanation:

Given

`A (x_1,y_1) = (40,20)`

`B (x_2,y_2) = (80,20)`

`C (x_3,y_3) = (100,70)`

`D (x_4,y_4) = (40,70)`

Required

Determine the Area

The area of the section is:

`Area = (1)/(2)|(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1)|`

Substitute values for the x's and y's

`Area = (1)/(2)|(40 * 20 + 80*70 + 100*70 + 40*40) - (20*80 + 20*100 + 70*40 + 70*40)|`

`Area = (1)/(2)|15000 - 9200|`

`Area = (1)/(2)|5800|`

`Area = (1)/(2) * 5800`

`Area = 2900`

Hence, the area of the section is 2900ft^2