Question

find the perimeter and area of rectangle abcd if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary. a(-2,7) b(4,4) c(2,0) d(-4,3)

Explanation:

Step1: Calculate the length of side AB using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

For points $A(-2,7)$ and $B(4,4)$, we have $x_1=-2,y_1 = 7,x_2=4,y_2 = 4$. Then $AB=\sqrt{(4 + 2)^2+(4 - 7)^2}=\sqrt{36 + 9}=\sqrt{45}=3\sqrt{5}\approx 6.7$ cm.

Step2: Calculate the length of side BC using the distance formula.

For points $B(4,4)$ and $C(2,0)$, we have $x_1 = 4,y_1=4,x_2=2,y_2 = 0$. Then $BC=\sqrt{(2 - 4)^2+(0 - 4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.5$ cm.

Step3: Calculate the perimeter of the rectangle.

The perimeter $P$ of a rectangle is $P = 2(AB + BC)$. Substituting the values of $AB$ and $BC$, we get $P=2(3\sqrt{5}+2\sqrt{5})=2\times5\sqrt{5}=10\sqrt{5}\approx 22.4$ cm.

Step4: Calculate the area of the rectangle.

The area $A$ of a rectangle is $A=AB\times BC$. Substituting the values of $AB$ and $BC$, we get $A = 3\sqrt{5}\times2\sqrt{5}=30$ $cm^2$.

Answer:

Perimeter: $22.4$ cm, Area: $30$ $cm^2$