Examples with solutions for Area of a Triangle: Calculate The Missing Side based on the formula

Exercise #1

Calculate X using the data in the figure below.

S=20S=20S=20555XXXAAABBBCCC

Video Solution

Step-by-Step Solution

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=AB×AC2 20=\frac{AB\times AC}{2}

20=x×52 20=\frac{x\times5}{2}

Multiply by 2 to get rid of the fraction:

5x=40 5x=40

Divide both sections by 5:

5x5=405 \frac{5x}{5}=\frac{40}{5}

x=8 x=8

Answer

8

Exercise #2

The area of triangle ABC is 20 cm².

Its height (AD) is 8.

Calculate the length of the side BC.

S=20S=20S=20888AAACCCBBBDDD

Video Solution

Step-by-Step Solution

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

S=AD×BC2 S=\frac{AD\times BC}{2}

20=8×BC2 20=\frac{8\times BC}{2}

Cross multiplication:

40=8BC 40=8BC

Divide both sides by 8:

408=8BC8 \frac{40}{8}=\frac{8BC}{8}

BC=5 BC=5

Answer

5 cm

Exercise #3

PRS is a triangle.

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

Calculate the height PQ.

S=30S=30S=30444PPPRRRSSSQQQ

Video Solution

Step-by-Step Solution

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!

SideHeight2=Triangular Area \frac{Side\cdot Height}{2}=\text{Triangular Area}

Double the equation by a common denominator:

4PQ2=30 \frac{4\cdot PQ}{2}=30

2 \cdot2

Divide the equation by the coefficient of PQ PQ .

4PQ=60 4PQ=60 / :4 :4

PQ=15 PQ=15

Answer

15 cm

Exercise #4

ABC is a right triangle with an area of 40.

Calculate the length of side BC.

404040101010AAABBBCCC

Video Solution

Answer

8

Exercise #5

ABC is a right triangle with an area of 32.

Calculate the length of side BC.

323232888AAABBBCCC

Video Solution

Answer

8

Exercise #6

Look at the right triangle below.

Area = 10

How long is side BC?

101010444AAABBBCCC

Video Solution

Answer

5

Exercise #7

The area of triangle DEF is 70 cm².

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

S=70S=70S=70141414DDDFFFEEE

Video Solution

Answer

10 cm

Exercise #8

ABC is a right triangle with an area of 36.

Calculate the length of side BC.

363636121212AAABBBCCC

Video Solution

Answer

6

Exercise #9

ABC is a right triangle with an area of 21.

Calculate the length of side BC.

212121777AAABBBCCC

Video Solution

Answer

6

Exercise #10

A right triangle is shown below.

Its area is 10.5.

Calculate the length of side BC.

10.510.510.5333AAABBBCCC

Video Solution

Answer

7

Exercise #11

ABC right triangle with an area of 27.

How long is side BC?

272727999AAABBBCCC

Video Solution

Answer

6

Exercise #12

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

Calculate the length of side BC.

777222AAABBBCCC

Video Solution

Answer

7

Exercise #13

The area of the triangle DEF is 60 cm².

The length of the side FE = 12.

Calculate the height DH.

S=60S=60S=60121212DDDEEEFFFHHH

Video Solution

Answer

10 cm

Exercise #14

The triangle ABC is a right triangle.

The area of the triangle is 38 cm².

AC = 8

Calculate side BC.

S=38S=38S=38888AAABBBCCC

Video Solution

Answer

9.5 cm

Exercise #15

Calculate X using the data in the figure below.

S=18.5S=18.5S=18.5XXX101010AAABBBCCC

Video Solution

Answer

3.7

Exercise #16

Calculate X using the data in the figure below.

S=8.375S=8.375S=8.375XXX2.52.52.5AAABBBCCC

Video Solution

Answer

6.7

Exercise #17

DEF is a right triangle.

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

Calculate the length of side DF.

S=40S=40S=40101010DDDEEEFFFGGG

Video Solution

Answer

8 cm

Exercise #18

Calculate X using the data in the figure below.

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

Video Solution

Answer

3

Exercise #19

Triangle ABC is isosceles.

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

Calculate the length AD.

S=60S=60S=60AAACCCBBBDDD5

Video Solution

Answer

12 cm