MATH SOLVE

4 months ago

Q:
# What is the area of this figure? Enter your answer in the box. units² An irregular heptagon is graphed on a coordinate plane. The horizontal x-axis ranges from negative 6 to 6 in increments of 1. The vertical y-axis ranges from negative 6 to 6 in increments of 1. The vertices of the heptagon are located at begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair negative 4 comma 5 end ordered pair, begin ordered pair negative 2 comma 3 end ordered pair, begin ordered pair 3 comma 4 end ordered pair, begin ordered pair 4 comma 3 end ordered pair, begin ordered pair 4 comma negative 3 end ordered pair, and begin ordered pair negative 3 comma negative 3 end ordered pair.

Accepted Solution

A:

We divide the figure in the following areas:

Area of the two upper triangles:

Area of triangle 1:

At1 = (1/2) * (3) * (2) = 3

Area of triangle 2:

At2 = (1/2) * (6) * (1) = 3

Area of the complete lower rectangle

Ar = (9) * (6) = 54

Area of the lower triangle:

At3 = (1/2) * (2) * (6) = 6

The total area of the figure is:

At1 + At2 + Ar-At3 = (3) + (3) + (54) - (6) = 54

answer:

the area of this figure is 54 units^2

Area of the two upper triangles:

Area of triangle 1:

At1 = (1/2) * (3) * (2) = 3

Area of triangle 2:

At2 = (1/2) * (6) * (1) = 3

Area of the complete lower rectangle

Ar = (9) * (6) = 54

Area of the lower triangle:

At3 = (1/2) * (2) * (6) = 6

The total area of the figure is:

At1 + At2 + Ar-At3 = (3) + (3) + (54) - (6) = 54

answer:

the area of this figure is 54 units^2