Question

Find the perimeter and area of the given triangle:

Answer 1

Answer:

The perimeter is 13.213 units.

The area is 7 square units

Step-by-step explanation:

O=(0,0)=(xo,yo)→xo=0, yo=0

A=(5,2)=(xa,ya)→xa=5, ya=2

B=(3,4)=(xb,yb)→xb=3, yb=4

Perimeter: P=OA+AB+OB

$OA=\sqrt{(xa-xo)^{2}+(ya-yo)^{2}}\\ OA=\sqrt{(5-0)^{2}+(2-0)^{2}}\\ OA=\sqrt{(5)^{2}+(2)^{2}}\\ OA=\sqrt{25+4}\\ OA=\sqrt{29}$

$AB=\sqrt{(xb-xa)^{2}+(yb-ya)^{2}}\\ AB=\sqrt{(3-5)^{2}+(4-2)^{2}}\\ AB=\sqrt{(-2)^{2}+(2)^{2}}\\ AB=\sqrt{4+4}\\ AB=\sqrt{8}\\ AB=\sqrt{4*2}\\ AB=\sqrt{4}\sqrt{2}\\ AB=2\sqrt{2}$

$OB=\sqrt{(xb-xo)^{2}+(yb-yo)^{2}}\\ OB=\sqrt{(3-0)^{2}+(4-0)^{2}}\\ OB=\sqrt{(3)^{2}+(4)^{2}}\\ OB=\sqrt{9+16}\\ OB=\sqrt{25}\\ OB=5$

P=OA+AB+OB

P=√29+2√2+5

P=5.385+2(1.414)+5

P=5.385+2.828+5

P=13.213

Area: A

$A=\frac{x_{o} y_{a}+x_{a} y_{b}+x_{b} y_{o}-(y_{o} x_{a}+y_{a} x_{b}+y_{b} x_{o}) }{2}$

$A=\frac{(0)(2)+(5)(4)+(3)(0)-[(0)(5)+(2)(3)+(4)(0)] }{2}$

$A=\frac{0+20+0-(0+6+0)}{2}\\ A=\frac{20-(6)}{2}\\ A=\frac{20-6}{2}\\ A=\frac{14}{2}\\ A=7$