Examples with solutions for Area of a Triangle: Subtraction or addition to a larger shape

Exercise #1

The quadrilateral ABCD is a rectangle.

Points E and F are located on sides DC and BC respectively.

FC = 1.5 cm
EC = 5 cm
DE = 3 cm

AD = 4 cm

Calculate the area of the quadrilateral ABFE.

4443335551.51.51.5AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

Let's calculate the side DC:

3+5=8 3+5=8

Now we can calculate the area of square ABCD:

4×8=32 4\times8=32

Let's calculate the area of triangle ADE:

4×32=122=6 \frac{4\times3}{2}=\frac{12}{2}=6

Let's calculate the area of triangle FCE:

5×1.52=7.52=3.75 \frac{5\times1.5}{2}=\frac{7.5}{2}=3.75

Now let's calculate the area of AEFB by subtracting the other areas we found:

AEFB=3263.75=22.25 AEFB=32-6-3.75=22.25

Answer

22.25

Exercise #2

Given the triangle ABC whose area is 95 cm².

Given DFBE parallelogram
DH is the height of the triangle AFD

AB=13 DH=6 AF=5

What is the area of the triangle DEC?

S=95S=95S=95131313666AAABBBCCCDDDEEEFFFHHH5

Video Solution

Answer

32 cm²

Exercise #3

In a square-shaped recreation space, they want to paint part of it white so that the shape of the white paint is triangular.

The length of the play area is 6 meters

one box of paint is required for each meter of paint.

How many buckets of paint do you need to paint the triangular area?

666

Video Solution

Answer

18 paint boxes

Exercise #4

Below is the trapezoid ABCD.

AB = 5 cm

DC = 10 cm

EC = 2 cm

AF = 4 cm
AF is perpendicular to DC.

Calculate the area of the quadrilateral ABCE.

555101010444222AAABBBCCCDDDEEEFFF

Video Solution

Answer

14

Exercise #5

The shape below consists of a rectangle from which the line segment BH has been erased.

AB = 6 cm

AH = 7 cm

EF = 3 cm

HG = 12 cm

BC = 3 cm


Calculate the area of the shape shaded orange.

666777333121212333333AAABBBCCCDDDHHHGGGFFFEEE

Video Solution

Answer

43.5 cm

Exercise #6

The drawing shows an equilateral triangle

The length of each of its sides 7 cm

a semicircle is placed on each side of each side

What is the area of the entire shape? Replace π=3.14 \pi=3.14

777777777

Video Solution

Answer

78.91 cm².