Area of a Triangle: Using additional geometric shapes

Question 1

The trapezoid ABCD and the rectangle ABGE are shown in the figure below.

Given in cm:

AB = 5

BC = 5

GC = 3

Calculate the area of the rectangle ABGE.

Question 2

Given the rectangle ABCD

Given BC=X and the side AB is larger by 4 cm than the side BC.

The area of the triangle ABC is 8X cm².

What is the area of the rectangle?

Question 3

The parallelogram ABCD and the triangle BCE are shown below.

CE = 7
DE = 15

The area of the triangle BCE is equal to 14 cm².

Calculate the area of the parallelogram ABCD.

Question 4

AD is perpendicular to BC

AD=3

The area of the triangle ABC is equal to 7 cm².

BC is the diameter of the circle on the drawing

What is the area of the circle?
Replace $\pi=3.14$

Question 5

ABCD is a parallelogram.

AD is the diameter of a circle that has a circumference of $7\pi$ cm.

Express the area of triangle EBC in terms of X.

Examples with solutions for Area of a Triangle: Using additional geometric shapes

Exercise #1

The trapezoid ABCD and the rectangle ABGE are shown in the figure below.

Given in cm:

AB = 5

BC = 5

GC = 3

Calculate the area of the rectangle ABGE.

Video Solution

Step-by-Step Solution

Let's calculate side BG using the Pythagorean theorem:

$BG^2+GC^2=BC^2$

We'll substitute the known data:

$BG^2+3^2=5^2$

$BG^2+9=25$

$BG^2=16$

$BG=\sqrt{16}=4$

Now we can calculate the area of rectangle ABGE since we have the length and width:

$5\times4=20$

Answer

Exercise #2

Given the rectangle ABCD

Given BC=X and the side AB is larger by 4 cm than the side BC.

The area of the triangle ABC is 8X cm².

What is the area of the rectangle?

Video Solution

Step-by-Step Solution

Let's calculate the area of triangle ABC:

$8x=\frac{(x+4)x}{2}$

Multiply by 2:

$16x=(x+4)x$

Divide by x:

$16=x+4$

Let's move 4 to the left side and change the sign accordingly:

$16-4=x$

$12=x$

Now let's calculate the area of the rectangle, multiply the length and width where BC equals 12 and AB equals 16:

$16\times12=192$

Answer

192

Exercise #3

The parallelogram ABCD and the triangle BCE are shown below.

CE = 7
DE = 15

The area of the triangle BCE is equal to 14 cm².

Calculate the area of the parallelogram ABCD.

Video Solution

Answer

32 cm²

Exercise #4

AD is perpendicular to BC

AD=3

The area of the triangle ABC is equal to 7 cm².

BC is the diameter of the circle on the drawing

What is the area of the circle?
Replace $\pi=3.14$

Video Solution

Answer

17.1 cm².

Exercise #5

ABCD is a parallelogram.

AD is the diameter of a circle that has a circumference of $7\pi$ cm.

Express the area of triangle EBC in terms of X.

Video Solution

Answer

$3.5X + 7 cm²$

Question 1

ACDE is a parallelogram.

DE = 12

A semicircle is placed on side FB.

If the area of the semicircle is $9\pi$ , then what is the area of triangle ABC?

Question 2

Given the triangle ABC and the deltoid ADEF

The height of the triangle is 4 cm

The base of the triangle is greater by 2 than the height of the triangle.

Segment FD cut to the middle

Calculate the area of the deltoid ADEF

Question 3

Given the triangle ABC when the base BC a semi-circle is drawn

The radius of the circle is equal to 3 cm and its center is the point D

Given AE=3 ED

What is the area of the dotted shape?

Question 4

The height of the house in the drawing is $$ 12x+9 $$

its width $$ x+2y $$

Given the ceiling height is half the height of the square section.

Express the area of the house shape in the drawing band x and and.

Question 5

Look at the triangle in the figure.

AD is used to form a semicircle with a radius of 2.5 cm.

Calculate the area of the triangle ABC.

Exercise #6

ACDE is a parallelogram.

DE = 12

A semicircle is placed on side FB.

If the area of the semicircle is $9\pi$ , then what is the area of triangle ABC?

Video Solution

Answer

$36\sqrt{2}$ cm²

Exercise #7

Given the triangle ABC and the deltoid ADEF

The height of the triangle is 4 cm

The base of the triangle is greater by 2 than the height of the triangle.

Segment FD cut to the middle

Calculate the area of the deltoid ADEF

Video Solution

Answer

8 cm²

Exercise #8

Given the triangle ABC when the base BC a semi-circle is drawn

The radius of the circle is equal to 3 cm and its center is the point D

Given AE=3 ED

What is the area of the dotted shape?

Video Solution

Answer

$36-\text{4}.5\pi$ cm².

Exercise #9

The height of the house in the drawing is $12x+9$

its width $x+2y$

Given the ceiling height is half the height of the square section.

Express the area of the house shape in the drawing band x and and.

Video Solution

Answer

$3x^2+8xy+1\frac{1}{2}x+4y^2+3y$

Exercise #10

Look at the triangle in the figure.

AD is used to form a semicircle with a radius of 2.5 cm.

Calculate the area of the triangle ABC.

Video Solution

Answer

$5\sqrt{14}+30$ cm².

Question 1

Given the trapezoid ABCD whose area is equal to 50 cm².

AB=7 DC=13

The area of the circle whose diameter FC is $2.25\pi$

How large is the area of the triangle AFD

Exercise #11

Given the trapezoid ABCD whose area is equal to 50 cm².

AB=7 DC=13

The area of the circle whose diameter FC is $2.25\pi$

How large is the area of the triangle AFD

Video Solution

Answer

25 cm²..