Question

Given A(-2,0); B(2,0); C(4,3); D(0,4); and E(-4,3) find the area and perimeter

Answer 1

Answer:

The area is 20 and perimeter is 19.4

Step-by-step explanation:

The given points will be plot on graph as shown in figure-1  

To calculate the area of this figure,

we divide this pentagon into 5 equal parts (figure-2)

we calculate area of  only one part and then multiply with 5 to get area of pentagon.

we can see in figure-2 , base is shown by green line which is '4' and height is shown by red line which is '2'

so, the area of triangle is calculated by $\frac{1}{2}\times\text{height}\times{base}$

$A=\frac{1}{2}\times2\times4$

$A=4$

therefore, the total area of pentagon is A=5*4 = 20

To calculate the perimeter of pentagon;

Parameter = Add all the sides of pentagon

to find the length of sides of polygon by using distance formula;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

distance between (-4,3) & (-2,0) =(4,3) & (2,0) = $\sqrt{(-2-(-4))^2+(0-3)^2}$

=$\sqrt{(2)^2+(-3)^2}$

=$\sqrt{4+9}$

=$\sqrt{13}$

=√13

distance between (0,4) & (4,3) =(0,4) & (-4,3) = $\sqrt{(4-(0))^2+(3-4)^2}$

=$\sqrt{(4)^2+(1)^2}$

=$\sqrt{16+1}$

=$\sqrt{17}$

=√17

and distance between (-2,0) & (2,0) is 4

So, Parimeter 'P' ;

P= 2*√17 + 2*√13 + 4

P= 2*√17 + 2*√13 + 4

P= 8.246 + 7.21 + 4

P = 19.4

Hence area is 20 and perimeter is 19.4

Answer 2

Answer:

If you graph the points and count the length you would get bases, 4 and 8 and the height 3

split it in two triangles like this http://prntscr.com/mtt4sq

then the triangle area formula base*height/2

8*3/2 = 12

4*3/2= 6

12+6=18

Now if we add the top triangle/s.   b*h/2

8*1/2=4

There are two triangles. The top half would equal 8.

18+8=26

The area would be 26

For perimeter:

We just need to find the hypotenuse since we know the height and the base of the triangle in the corner the base is 2. http://prntscr.com/mtt5bx

Using a2+b2=c2

2^2+3^2=c^2

4+9=13^2

13^2=3.6

Now we know all 4 sides.

3.6+3.6+4=11.2

This is for the bottom half total.

For the top triangle hypotenuse:    a^2+b^2=c^2

4^2+1^2=c^2

16+1=c^2

17^2=4.1

11.2+8.2= 19.4

The perimeter is 19.4

Hope this helped. :)