Question

critical thinking
find the perimeter and area of the rectangle.
(-4, 4)
(2, 4)
(-4, 0)
(2, 0)
find the circumference and area of the circle

Explanation:

Step1: Calculate the length of the rectangle

The length $l$ of the rectangle is the distance between $(-4,4)$ and $(2,4)$. Using the distance formula for points on a horizontal line (since the $y$-coordinates are the same), $l=\vert2 - (-4)\vert=6$.

Step2: Calculate the width of the rectangle

The width $w$ of the rectangle is the distance between $(-4,4)$ and $(-4,0)$. Using the distance formula for points on a vertical line (since the $x$-coordinates are the same), $w=\vert4 - 0\vert = 4$.

Step3: Calculate the perimeter of the rectangle

The perimeter $P$ of a rectangle is given by the formula $P = 2(l + w)$. Substituting $l = 6$ and $w=4$, we get $P=2(6 + 4)=20$.

Step4: Calculate the area of the rectangle

The area $A$ of a rectangle is given by the formula $A=l\times w$. Substituting $l = 6$ and $w = 4$, we get $A=6\times4 = 24$.

Answer:

Perimeter: 20
Area: 24