Polygon ABCDE is shown on the coordinate grid. What is the perimeter, to the nearest hundredth of a unit, of polygon ABCDE?

The perimeter of polygon ABCDE is 20.31 units.

Step-by-step explanation:

Step 1; First we plot points A, B, C, D and E on the graph. Coordinates are A (-3, 2), B (1, 2), C (3, -1), D(0, -3) and E (-4, -3). We need to find the distance between the 5 sides of the polygon i.e AB, BC, CD, DE, and AE.

Step 2; The sides AB and AE can be measured directly as they are horizontal lines. The x coordinate for A is -3 while for B it is 1, so distance is 1-(-3) = 4 units. The x coordinate for E is -4 while for D it is 0, so the distance is 0- (-4) = 4 units.

Step 3; To find the distances of BC, CD, and AE we use the formula

Distance = √ (x2 - x1)² + (y2 - y1)².

Distance between B (1, 2) and C (3, -1) where B is (x1, y1) and C is (x2, y2).

Distance = √(3 - 1)² + (-1 -2)² = √4 + 9 = √13 = 3.605 units.

Distance between C (3, -1) and D (0, -3) where C is (x1, y1) and D is (x2, y2).

Distance = √(0 -3)² + (-3 -(-1))² = √9 + 4 = √13 = 3.605 units.

Distance between A (-3, 2) and E (-4, -3) where D is (x1, y1) and E is (x2, y2).

Distance = √(-4 -(-3))² + (-3 -2)² = √1 + 25 = √26 = 5.099 units.

Step 2; The parameter of this polygon is given by summing the lengths of the 4 sides.

Parameter = AB + BC + CD + DE + AE = 4 + 3.605 + 3.605 + 4 + 5.099 = 20.309 units. This is rounded off to 20.31 units.

answer: -2+√x,-2-√x

i hope this , i don't know if you're looking for a pair or not.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.