Area of a Parallelogram: Using ratios for calculation

$$$$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.

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

$\frac{A_{AED}}{A_{ABCE}}=\frac{1}{3}$

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:

$A_{ADE}=\frac{h\times DE}{2}$

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

$A_{ABCD}=h\times EC$

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

$\frac{\frac{1}{2}h\times DE}{h\times EC}=\frac{1}{3}$

We solve by cross multiplying and obtain the formula:

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

We open the parentheses accordingly:

$h\times EC=1.5h\times DE$

We divide both sides by h:

$EC=\frac{1.5h\times DE}{h}$

We simplify to h:

$EC=1.5DE$

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

$1:1.5$

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

What is the area of the parallelogram?

$43.75$ cm².

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

Calculate the area of the parallelogram ABCD.

$112$ cm².

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.

15 cm

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.

$2.5$ cm

The parallelogram ABCD is shown below.

Its area is equal to 98 cm².

$\frac{AE}{DC}=\frac{1}{2}$

Calculate DC.

$14$ cm

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.

$x^2$

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.

Calculate the ratio between sides DE and EC.

1

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

63 cm².