Figure abcde has vertices a(−2, 3), b(2, 3), c(5, −2), d(0, −3), and e(−2, −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? part b: use figure abcde created on your coordinate grid to find the lengths, in units, of sides ab and ae. part c: what is the area of figure abcde? show your work. (20 points)

we plot the points a(−2, 3), b(2, 3), c(5, −2), d(0, −3), and e(−2, −2) and join the points in order ,

we get the figure as shown in the figure attached.

now we have to decompose it in rectangles and triangles

so we can see that we get 1 rectangle and 2 triangles.

part a : we get 1 rectangle and 2 triangles.

part b : we have to find the length of sides ab and ae

we can count the number of blocks , 1 block equals 1 unit

so , ab = 8 units , ae = 10 units

part c : we have to find the area of figure

so what we do is we find the area of rectangle and two triangles separately and add the areas , so we will get the complete area.

so area of rectangle = length * width = 10*8 = 80 square units.

area of pink triangle = 1/2 * base* height = 1/2 * 14 * 2 = 14 square units

area of yellow triangle = 1/2 * base * height = 1/2 * 10 * 6 = 30 square units

now total area of figure abcde = ( 80 + 14+ 30) square units

= 124 square units