Question

Find the area of the polygon with vertices P(5,-1), Q(-1,-4), R(-3,1), and S(0,3). If necessary, round

to the nearest tenth.

Answer 1

14.3 sq units

Explanation:

this shape is a trapezoid so we need to find height and each parallel base

to find height we can take the midpoint of RS and the midpoint of QP and then find the distance between each midpoint

midpoint of RS = (-3/2,2)

midpoint of QP = (2,-5/2)

distance between the two is 16/2 or 8

d(RS) = √2²+3² =
`√(13)`

d(QP) = √3²+6² = √45 =
`√(9)`
`√(5)` or 3
`√(5)`

put values into the formula for area:

A = 1/2(8) + (
`√(13)` + 3
`√(5)`)

A = 4 + (
`√(13)` + 3
`√(5)`)

A ≈ 14.3