Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles. Part A: How many triangles and rectangles did you make? (1 point)

Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points)

Part C: What is the area of Figure ABCDE? Show your work. (5 points)

Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2).

To Find : Plot the points  

Decompose Figure ABCDE into rectangles and triangles.

lengths of Sides AB and AE.

area of Figure ABCDE

Solution:

Plot ( x , y)

if x is +ve go right from origin if negative then go left

for y go upward if +ve , in case of -ve go downward

Points plotted and labelled

A(−3, 3), B(2, 3),

length of AB =  5

A(−3, 3) E(−3, −2).

Length of AE = 5

One rectangle and two triangle

area of rectangle  = 5 * 5  = 25 sq units

area of right angle triangle = (1/2) * 5 * 3  = 7.5 sq units

area of another triangle = (1/2) * 8 * 1 = 4 Sq units

Area of figure  = 25 + 7.5 + 4  = 36.5 sq units

Learn More:

locate the points A (1, 2), B( 3, 4) and C

Locate 4x+y=10.find the coordinates of the point where the graph ...

Step-by-step explanation:

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.