Question

What is the area of the composite figure whose vertices have the following coordinates? (−2, −2) , (3, −2) , (5, −4) , (1, −8) , (−2, −4) Enter your answer in the box.

Answer 1

The area of the composite figure is:

26 square units.

Explanation:

The area of the composite figure is equal to:

Area of rectangle ABEI+Area of ΔBIC+Area of ΔDHC+Area of ΔDHE.

Now,

In rectangle ABEI:

Length(l)=5 units.

breadth(b)=2 units.

Area of rectangle ABEI=l×b

=5×2=10 square units.

In ΔBIC:

Base(b)=2 units.

Height(h)=2 units.

Area of ΔBIC=(1/2)×b×h

=(1/2)×2×2=2 square units.

In ΔDHC:

Base(b)=4 units.

Height(h)=4 units.

Area of ΔDHC=(1/2)×b×h

=(1/2)×4×4=8 square units.

In ΔDHE:

Base(b)=3 units.

Height(h)=4 units.

Area of ΔDHC=(1/2)×b×h

=(1/2)×3×4=6 square units.

Hence, area of figure formed by these points=10+2+6+8

=26 square units.

Answer 2

Area of a rectangle = W X L
Area of a rectangle = 5 X 2
Area of a rectangle = 10

Area of triangle 1= 1/2 X B X H
Area of triangle 1= 1/2 X 2 X 2
Area of triangle 1= 1/2 X 4
Area of triangle 1= 2

Area of triangle 2= 1/2 X B X H
Area of triangle 2= 1/2 X 7 X 4
Area of triangle 2= 1/2 X 28
Area of triangle 2= 14

Area of a rectangle + Area of triangle 1 + Area of triangle 2=

10 + 2 + 14 = 36