Area of a Triangle: Subtraction or addition to a larger shape

Question 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.

Question 2

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.

Question 3

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.

Question 4

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?

Question 5

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?

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.

Video Solution

Step-by-Step Solution

Let's calculate the side DC:

$3+5=8$

Now we can calculate the area of square ABCD:

$4\times8=32$

Let's calculate the area of triangle ADE:

$\frac{4\times3}{2}=\frac{12}{2}=6$

Let's calculate the area of triangle FCE:

$\frac{5\times1.5}{2}=\frac{7.5}{2}=3.75$

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

$AEFB=32-6-3.75=22.25$

Answer

22.25

Exercise #2

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.

Video Solution

Step-by-Step Solution

Let's first calculate the area of triangle ABC:

$\frac{6\times7}{2}=\frac{42}{2}=21$

Since the shape before us is a rectangle, we can claim that:

AC=GD=7

Now let's calculate the area of triangle HGD:

$\frac{7\times3}{2}=\frac{21}{2}=10.5$

Let's draw an imaginary line between B and H to get square BEFH where each side equals 3 cm.

Let's calculate the area of BEFH:

$3\times3=9$

Let's calculate the area of rectangle ACDG:

$7\times12=84$

Now we can calculate the area of the brown shape by subtracting the other areas we found:

Answer

43.5 cm

Exercise #3

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.

Video Solution

Answer

Exercise #4

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?

Video Solution

Answer

32 cm²

Exercise #5

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?

Video Solution

Answer

18 paint boxes

Question 1

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 $\pi=3.14$

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 $\pi=3.14$

Video Solution

Answer

78.91 cm².