Question

find the area of quadrilateral rstu. s(-4, 4) t(3, 3) r(-4, -1) u(2, -1) square units

Explanation:

Step1: Divide the quadrilateral

We can divide quadrilateral $RSTU$ into a rectangle and a triangle. The rectangle is formed by points $R(-4,-1)$, $S(-4,4)$, $U(2,-1)$ and a point $(2,4)$. The triangle is above the rectangle with vertices $S(-4,4)$, $T(3,3)$ and $(2,4)$.

Step2: Calculate the area of the rectangle

The length of the rectangle along the $x -$axis is $2-(-4)=6$ and along the $y -$axis is $4 - (-1)=5$. The area of a rectangle $A_{rect}=l\times w$. So, $A_{rect}=6\times5 = 30$.

Step3: Calculate the area of the triangle

The base of the triangle is the horizontal distance between $S(-4,4)$ and $(2,4)$, which is $2-(-4)=6$. The height of the triangle is the vertical distance from $T(3,3)$ to the line $y = 4$, which is $4 - 3=1$. The area of a triangle $A_{tri}=\frac{1}{2}\times b\times h$. So, $A_{tri}=\frac{1}{2}\times6\times1=3$.

Step4: Calculate the area of the quadrilateral

The area of the quadrilateral $A = A_{rect}+A_{tri}$. So, $A=30 + 3=33$.

Answer:

33