Area of a Triangle: Calculate The Missing Side based on the formula

Calculate X using the data in the figure below.

The formula to calculate the area of a triangle is:

(side * height descending from the side) /2

We place the data we have into the formula to find X:

$20=\frac{AB\times AC}{2}$

$20=\frac{x\times5}{2}$

Multiply by 2 to get rid of the fraction:

$5x=40$

Divide both sections by 5:

$\frac{5x}{5}=\frac{40}{5}$

$x=8$

8

The area of triangle ABC is 20 cm².

Its height (AD) is 8.

Calculate the length of the side BC.

We can insert the given data into the formula in order to calculate the area of the triangle:

$S=\frac{AD\times BC}{2}$

$20=\frac{8\times BC}{2}$

Cross multiplication:

$40=8BC$

Divide both sides by 8:

$\frac{40}{8}=\frac{8BC}{8}$

$BC=5$

5 cm

PRS is a triangle.

The length of side SR is 4 cm.
The area of triangle PSR is 30 cm².

Calculate the height PQ.

We use the formula to calculate the area of the triangle.

Pay attention: in an obtuse triangle, the height is located outside of the triangle!

$$$\frac{Side\cdot Height}{2}=\text{Triangular Area}$

Double the equation by a common denominator:

$\frac{4\cdot PQ}{2}=30$

$\cdot2$

Divide the equation by the coefficient of $PQ$.

$4PQ=60$ / $:4$

$PQ=15$

15 cm

ABC is a right triangle with an area of 32.

Calculate the length of side BC.

8

A right triangle is shown below.

Its area is 10.5.

Calculate the length of side BC.

7

ABC is a right triangle with an area of of 7.

Calculate the length of side BC.

7

The area of the triangle DEF is 60 cm².

The length of the side FE = 12.

Calculate the height DH.

10 cm

The area of triangle DEF is 70 cm².

Calculate h given that the length of side FE is 14 cm.

10 cm

Look at the right triangle below.

Area = 10

How long is side BC?

5

ABC is a right triangle with an area of 36.

Calculate the length of side BC.

6

ABC is a right triangle with an area of 21.

Calculate the length of side BC.

6

ABC right triangle with an area of 27.

How long is side BC?

6

ABC is a right triangle with an area of 40.

Calculate the length of side BC.

8

The triangle ABC is a right triangle.

The area of the triangle is 38 cm².

AC = 8

Calculate side BC.

9.5 cm

Calculate X using the data in the figure below.

3.7

Calculate X using the data in the figure below.

6.7

DEF is a right triangle.

Height GE is 10 cm.
The area of DEF is 40 cm².

Calculate the length of side DF.

8 cm

Triangle ABC is isosceles.

AD is the median of the BC.
ABC has an area of 60 cm².
BD = 5

Calculate the length AD.

12 cm

Calculate X using the data in the figure below.

3

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.

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