Question

Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane. For the rectangle FROG, the perimeter is . Find the area of the rectangle FROG. For the rectangle FROG, the area is

Answer 1

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

where

L is the length of rectangle

W is the width of rectangle

we have

$F(-2,5),R(-2,1),O(6,1),G(6,5)$

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

so

$FG=RO=L\\RF=OG=W$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance FG

$F(-2,5),G(6,5)$

substitute the values

$d=\sqrt{(5-5)^{2}+(6+2)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$FG=8\ units$

step 2

Find the distance RF

$R(-2,1),F(-2,5)$

substitute the values

$d=\sqrt{(5-1)^{2}+(-2+2)^{2}}$

$d=\sqrt{(4)^{2}+(0)^{2}}$

$RF=4\ units$

step 3

Find the perimeter

$P=2(L+W)$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$P=2(8+4)=24\ units$

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

$A=LW$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$A=(8)(4)=32\ units^2$

Answer 2

The area and the perimeter of the rectangle FROG is evaluated as:

• Area(FROG) = $32 \: \rm unit^2$
• Perimeter(FROG) = $64\: \rm units$

How to find the area and the perimeter of a rectangle?

For a rectangle with length and width L and W units, we get:

• Area of the rectangle = $L \times W \: \rm unit^2$
• Perimeter of the rectangle = $2(L + W) \: \rm unit^2$

What is the distance between two points ( p,q) and (x,y)?

The shortest distance(straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

$D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.$

The coordinates of the points of the rectangle FROG are given as:

F(-2,5), R(-2,1), G(6,5), and O(6,1) (from its plot, as given below)

FR and RO are length and width pair(we can call any one of them as length and other as width) of the considered rectangle as they are adjacent to each other.

We denote length of a line segment AB by |AB|

Thus, we get:

• Length of the rectangle = |FR| = $\sqrt{(-2-(-2))^2 + (1 - 5)^2 } = 4$ units
• Width of the rectangle = |RO| = $\sqrt{(6-(-2))^2 + (1 - 1)^2 } = \sqrt{64} = 8 \: \rm units$

Now with the help of length and width, we can evaluate its perimeter and area, as shown below:

• Area(FROG) = $L\times W = 4 \times 8= 32 \: \rm unit^2$
• Perimeter(FROG) = $2(L + W) = 2(4 + 8) = 64\: \rm units$

Learn more about distance between two points here:

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