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

Ascertaining whether or not there are errors in the dataCalculating in two waysUsing congruence and similarityWorded problemsSubtraction or addition to a larger shapeHow many times does the shape fit inside of another shape?Using Pythagoras' theoremUsing ratios for calculationUsing additional geometric shapesUsing variablesFinding Area based off Perimeter and Vice VersaApplying the formula
Question 1

Calculate X using the data in the figure below.

S=20S=20S=20555XXXAAABBBCCC

Question 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

Question 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

Question 4

ABC is a right triangle with an area of 40.

Calculate the length of side BC.

404040101010AAABBBCCC

Question 5

ABC is a right triangle with an area of 32.

Calculate the length of side BC.

323232888AAABBBCCC

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!

Side⋅Height2=Triangular Area \frac{Side\cdot Height}{2}=\text{Triangular Area}

Double the equation by a common denominator:

4⋅PQ2=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

Question 1

Look at the right triangle below.

Area = 10

How long is side BC?

101010444AAABBBCCC

Question 2

The area of triangle DEF is 70 cm².

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

S=70S=70S=70141414DDDFFFEEE

Question 3

ABC is a right triangle with an area of 36.

Calculate the length of side BC.

363636121212AAABBBCCC

Question 4

ABC is a right triangle with an area of 21.

Calculate the length of side BC.

212121777AAABBBCCC

Question 5

A right triangle is shown below.

Its area is 10.5.

Calculate the length of side BC.

10.510.510.5333AAABBBCCC

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

Question 1

ABC right triangle with an area of 27.

How long is side BC?

272727999AAABBBCCC

Question 2

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

Calculate the length of side BC.

777222AAABBBCCC

Question 3

The area of the triangle DEF is 60 cm².

The length of the side FE = 12.

Calculate the height DH.

S=60S=60S=60121212DDDEEEFFFHHH

Question 4

The triangle ABC is a right triangle.

The area of the triangle is 38 cm².

AC = 8

Calculate side BC.

S=38S=38S=38888AAABBBCCC

Question 5

Calculate X using the data in the figure below.

S=18.5S=18.5S=18.5XXX101010AAABBBCCC

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

Question 1

Calculate X using the data in the figure below.

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

Question 2

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

Question 3

Calculate X using the data in the figure below.

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

Question 4

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

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