Question

find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary. a(0, 9) b(4, 9) c(0, 1)

Explanation:

Step1: Calculate length of AC

Use distance formula for points $A(0,9)$ and $C(0,1)$. Since $x$-coordinates are same, length $AC=\vert9 - 1\vert=8$ cm.

Step2: Calculate length of AB

For points $A(0,9)$ and $B(4,9)$, since $y$-coordinates are same, length $AB=\vert4 - 0\vert = 4$ cm.

Step3: Calculate length of BC

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for $B(4,9)$ and $C(0,1)$. Here $x_1 = 0,y_1 = 1,x_2=4,y_2 = 9$. So $BC=\sqrt{(4 - 0)^2+(9 - 1)^2}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}\approx8.9$ cm.

Step4: Calculate perimeter

Perimeter $P=AB + AC+BC=4 + 8+8.9 = 20.9$ cm.

Step5: Calculate area

Use area formula for a right - triangle $A=\frac{1}{2}\times base\times height$. Here base $AC = 8$ cm and height $AB = 4$ cm. So $A=\frac{1}{2}\times8\times4=16$ $cm^2$.

Answer:

perimeter: $20.9$ cm
area: $16$ $cm^2$