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

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

Exercise #5

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 #6

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 #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

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Video Solution

Answer

63 cm².