Area of a Triangle: Using ratios for calculation

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 additional geometric shapesUsing variablesFinding Area based off Perimeter and Vice VersaCalculate The Missing Side based on the formulaApplying the formula
Question 1

\( \)\( \)The area of trapezoid ABCD is X cm².

The line AE creates triangle AED and parallelogram ABCE.

The ratio between the area of triangle AED and the area of parallelogram ABCE is 1:3.

Calculate the ratio between sides DE and EC.

AAABBBCCCDDDEEE

Question 2

Since the side BC is \( \frac{1}{3} \) side AE.

Calculate the area of the triangle:

666AAABBBCCCEEE

Question 3

Since the side BC is \( \frac{1}{4} \) side AE.

Calculate the area of the triangle:

121212AAABBBCCCEEE

Question 4

Since the side BC is \( \frac{1}{5} \) side AE.

Calculate the area of the triangle:

101010AAABBBCCCEEE

Question 5

Since the side BC is \( \frac{2}{3} \) side AE.

Calculate the area of the triangle:

999AAABBBCCCEEE

Examples with solutions for Area of a Triangle: Using ratios for calculation

Exercise #1

The area of trapezoid ABCD is X cm².

The line AE creates triangle AED and parallelogram ABCE.

The ratio between the area of triangle AED and the area of parallelogram ABCE is 1:3.

Calculate the ratio between sides DE and EC.

AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

To calculate the ratio between the sides we will use the existing figure:

AAEDAABCE=13 \frac{A_{AED}}{A_{ABCE}}=\frac{1}{3}

We calculate the ratio between the sides according to the formula to find the area and then replace the data.

We know that the area of triangle ADE is equal to:

AADE=h×DE2 A_{ADE}=\frac{h\times DE}{2}

We know that the area of the parallelogram is equal to:

AABCD=h×EC A_{ABCD}=h\times EC

We replace the data in the formula given by the ratio between the areas:

12h×DEh×EC=13 \frac{\frac{1}{2}h\times DE}{h\times EC}=\frac{1}{3}

We solve by cross multiplying and obtain the formula:

h×EC=3(12h×DE) h\times EC=3(\frac{1}{2}h\times DE)

We open the parentheses accordingly:

h×EC=1.5h×DE h\times EC=1.5h\times DE

We divide both sides by h:

EC=1.5h×DEh EC=\frac{1.5h\times DE}{h}

We simplify to h:

EC=1.5DE EC=1.5DE

Therefore, the ratio between is: ECDE=11.5 \frac{EC}{DE}=\frac{1}{1.5}

Answer

1:1.5 1:1.5

Exercise #2

Since the side BC is 13 \frac{1}{3} side AE.

Calculate the area of the triangle:

666AAABBBCCCEEE

Video Solution

Answer

6

Exercise #3

Since the side BC is 14 \frac{1}{4} side AE.

Calculate the area of the triangle:

121212AAABBBCCCEEE

Video Solution

Answer

18

Exercise #4

Since the side BC is 15 \frac{1}{5} side AE.

Calculate the area of the triangle:

101010AAABBBCCCEEE

Video Solution

Answer

10

Exercise #5

Since the side BC is 23 \frac{2}{3} side AE.

Calculate the area of the triangle:

999AAABBBCCCEEE

Video Solution

Answer

27

Question 1

Since the side BC is \( \frac{5}{8} \) side AE.

Calculate the area of the triangle:

161616AAABBBCCCEEE

Question 2

The area of trapezoid ABCD

is 30 cm².

The line AE creates triangle AED and parallelogram ABCE.

The ratio between the area of triangle AED and the area of parallelogram ABCE is 1:2.

AAABBBCCCDDDEEE

Calculate the ratio between sides DE and EC.

Question 3

The area of the triangle below is equal to 10 cm² and its height is 5 times greater than its base.

Calculate X.

101010xxx

Exercise #6

Since the side BC is 58 \frac{5}{8} side AE.

Calculate the area of the triangle:

161616AAABBBCCCEEE

Video Solution

Answer

80

Exercise #7

The area of trapezoid ABCD

is 30 cm².

The line AE creates triangle AED and parallelogram ABCE.

The ratio between the area of triangle AED and the area of parallelogram ABCE is 1:2.

AAABBBCCCDDDEEE

Calculate the ratio between sides DE and EC.

Video Solution

Answer

1

Exercise #8

The area of the triangle below is equal to 10 cm² and its height is 5 times greater than its base.

Calculate X.

101010xxx

Video Solution

Answer

x=2 x=2