Examples with solutions for Area of a Triangle: Using variables

Exercise #1

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?

S=8XS=8XS=8XX+4X+4X+4XXXAAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's calculate the area of triangle ABC:

8x=(x+4)x2 8x=\frac{(x+4)x}{2}

Multiply by 2:

16x=(x+4)x 16x=(x+4)x

Divide by x:

16=x+4 16=x+4

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

164=x 16-4=x

12=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:

16×12=192 16\times12=192

Answer

192

Exercise #2

The area of the triangle is 16.

Calculate X.

444xxxAAABBBCCCEEE

Video Solution

Answer

8

Exercise #3

The area of the triangle is 9.

Calculate X.

333xxxAAABBBCCCEEE

Video Solution

Answer

6

Exercise #4

The area of the triangle below is equal to 21.

Calculate X.

777xxxAAABBBCCCEEE

Video Solution

Answer

6

Exercise #5

Since the area of the triangle is equal to 15.

Find X.

333xxxAAABBBCCCEEE

Video Solution

Answer

10

Exercise #6

The area of the triangle is 12.

Calculate X.

333xxxAAABBBCCCEEE

Video Solution

Answer

8

Exercise #7

Since the area of the triangle is equal to 15.

Find X.

555xxxAAABBBCCCEEE

Video Solution

Answer

6

Exercise #8

The area of the triangle below is equal to 3.

Calculate X.

222xxxAAABBBCCCEEE

Video Solution

Answer

3

Exercise #9

The area of the triangle is equal to 18.

Calculate X.

666xxxAAABBBCCCEEE

Video Solution

Answer

6

Exercise #10

Look at the triangle ABC below.

BC = 6

AD = X

Express the area of the triangle using X.

666XXXCCCAAABBBDDD

Video Solution

Answer

Answers B and C are correct.

Exercise #11

Calculate X using the data in the figure below.

S=22.5S=22.5S=22.5X+6X+6X+6555AAABBBCCC

Video Solution

Answer

3

Exercise #12

Express the area of the triangle ABC in terms of X.

2X2X2XAAABBBCCCDDD8X+1

Video Solution

Answer

X+923X22X1 \frac{X+9}{2}\sqrt{3X^2-2X-1}