Question

NO LINKS!! URGENT HELP!!

Calculate the perimeter of the following figures.

Answer 1

Quadrilateral: 20.5 units

Triangle: 8.6 units

Explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

`AB = √((-3 - (-3))^2 + ((-1) - 3)^2) = √(16) = 4`

`BC = √((-3 - 2)^2 + ((3) - 3)^2) = √(25)= 5`

`CD = √((2 - 4)^2 + ((3) - (-1))^2) = √(4+16) = 2√(5)`

`DA = √((4 - (-3))^2 + ((-1) - 1)^2) = √(49) =7`

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

=
`4+5+2\sqrt5+7=20.5` units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

`EF = √((-4 - (-2))^2 + ((1) - (3))^2) = 2√(2)`

`FG = √((-2 - (-2))^2 + ((3) - (4))^2) = 1`

`EG = √((-4 - (-2))^2 + ((1) - (4))^2) = √(4 + 9) = √(13)`

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 +
`√(13)`

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units