Find the perimeter and area of a polygon that has vertices at

H(-3, -2), I(5, -2), J(5, 7), K(-3, 7).

Perimeter of the polygon is 34 units.

Area of the polygon is 72 sq. units

Step-by-step explanation:

To find the perimeter and area, first we have to find the length of the 4 sides, using the distance formula.

H (-3,-2), I(5,-2), J (5,7), K (-3, 7)

Distance formula is given as √((x₂-x₁)² + (y₂-y₁)²)

HI = √ ((5-(-3))² + (-2-(-2))²)

   = √ ((8)² + (0)²) = √8² = 8

IJ = √((5-5)² +(7-(-2))²)

  = √9² = 9

JK = √((-3-5)² +(7-7)²) = √(-8)²

    = 8

KH = √((-3-(-3))² +(-2-7)²) = √(-9)² = 9

Perimeter = 2(l+ b ) = 2(9+8) = 34 units.

Area = l × b = 9 × 8 = 72 sq. units

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.