Examples with solutions for Area of a Trapezoid: 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.

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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

Look at the trapezoid ABCD below.

Length of side AB = a

Side DC is 3 cm longer than AB.

Height (h) = 12 \frac{1}{2} cm

Calculate the length of side AB, given that the area of the trapezoid is 2a cm².

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Video Solution

Answer

12 \frac{1}{2}

Exercise #3

The trapezoid ABCD is shown below.

AB = AD

DC is twice as long as AB.

The area of the trapezoid is three times more than the length of AB.

How long is side AB?

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Video Solution

Answer

2

Exercise #4

In the figure given the trapezoid ABCD

Given the ratio of the side AB to the height AE is 3:2

What is the area of the trapezoid?

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Video Solution

Answer

34 34 cm².

Exercise #5

The ratio between AB and DC is 3:4.

What is the area of the trapezoid?

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Video Solution

Answer

98 98 cm².

Exercise #6

The ratio between the height of the trapezoid and the small base is 1:15.

Find the area of the trapezoid.

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Video Solution

Answer

26 26 cm²

Exercise #7

Given that the ratio between the basis is 3:5

It is also given that the relationship between DC and AE is 2:1

Find the area of the trapezoid

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Video Solution

Answer

40 40 cm².

Exercise #8

The area of the trapezoid in the drawing is 30 cm².

The ratio between the two bases is 1:3.

What is the length of side DC?

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Video Solution

Answer

9 9 cm

Exercise #9

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.

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Calculate the ratio between sides DE and EC.

Video Solution

Answer

1