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.

14.3 sq units

Step-by-step 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 =

d(QP) = √3²+6² = √45 = or 3

put values into the formula for area:

A = 1/2(8) + ( + 3)

A = 4 + ( + 3)

A ≈ 14.3

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answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,