Area of a Parallelogram: Using ratios for calculation

Applying the formulaCalculate The Missing Side based on the formulaCalculating in two waysFinding Area based off Perimeter and Vice VersaUsing additional geometric shapesUsing congruence and similarityUsing external heightUsing Pythagoras' theoremUsing variablesVerifying whether or not the formula is applicable
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

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

What is the area of the parallelogram?

555AAABBBCCCDDDEEE

Question 3

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

Calculate the area of the parallelogram ABCD.

888AAABBBCCCDDDEEE

Question 4

Look at the parallelogram in the figure below.

The length of the height and side AB have a ratio of 4:1.

Express the area of the parallelogram in terms of X.

2X2X2XAAABBBCCCDDD

Question 5

The area of the parallelogram ABCD is equal to 150 cm².

AK is perpendicular to DC.

DC is 1.5 times longer than AK.

Calculate DC.

S=150S=150S=150AAABBBCCCDDDKKK

Examples with solutions for Area of a Parallelogram: 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

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

What is the area of the parallelogram?

555AAABBBCCCDDDEEE

Video Solution

Answer

43.75 43.75 cm².

Exercise #3

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

Calculate the area of the parallelogram ABCD.

888AAABBBCCCDDDEEE

Video Solution

Answer

112 112 cm².

Exercise #4

Look at the parallelogram in the figure below.

The length of the height and side AB have a ratio of 4:1.

Express the area of the parallelogram in terms of X.

2X2X2XAAABBBCCCDDD

Video Solution

Answer

x2 x^2

Exercise #5

The area of the parallelogram ABCD is equal to 150 cm².

AK is perpendicular to DC.

DC is 1.5 times longer than AK.

Calculate DC.

S=150S=150S=150AAABBBCCCDDDKKK

Video Solution

Answer

15 cm

Question 1

The parallelogram ABCD is shown below.

Its area is equal to 98 cm².

\( \frac{AE}{DC}=\frac{1}{2} \)

Calculate DC.

AAABBBCCCDDDEEE

Question 2

Look at the parallelograms in the figure.

The area of parallelogram ABCD divided by the area of parallelogram EFGH is equal to \( \frac{3}{1} \).

Calculate the length of EI.

S=45S=45S=45666AAABBBCCCDDDEEEFFFGGGHHHIII

Question 3

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 4

Triangle BDE an isosceles

DEFA parallelogram FC=6

Point E divides BC by 2:3 (BE>EC)

The height of the trapezoid DEFA for the side AF is equal to 7 cm

Calculate the area of the parallelogram DEFA

666777DDDEEEFFFAAACCCBBB

Exercise #6

The parallelogram ABCD is shown below.

Its area is equal to 98 cm².

AEDC=12 \frac{AE}{DC}=\frac{1}{2}

Calculate DC.

AAABBBCCCDDDEEE

Video Solution

Answer

14 14 cm

Exercise #7

Look at the parallelograms in the figure.

The area of parallelogram ABCD divided by the area of parallelogram EFGH is equal to 31 \frac{3}{1} .

Calculate the length of EI.

S=45S=45S=45666AAABBBCCCDDDEEEFFFGGGHHHIII

Video Solution

Answer

2.5 2.5 cm

Exercise #8

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 #9

Triangle BDE an isosceles

DEFA parallelogram FC=6

Point E divides BC by 2:3 (BE>EC)

The height of the trapezoid DEFA for the side AF is equal to 7 cm

Calculate the area of the parallelogram DEFA

666777DDDEEEFFFAAACCCBBB

Video Solution

Answer

63 cm².