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ACT Math : How to find the area of a quadrilateral

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Example Question #1 : How To Find The Area Of A Quadrilateral

Jane plans to re-tile her kitchen with tiles that have a length of inches and a width of inches wide. If her kitchen measures feet by feet, how many tiles will she need?

Possible Answers:

180

338

Correct answer:

338

Explanation:

When attempting to solve how many pieces of a particular object you need to cover a certain area, always make sure that your units of measurement (for the object and for the area you are covering) are the same. In the case of this question, the units of measurement are different, so you must first convert all measurements to use the same unit.

Since the tiles being used to cover the area are measured in inches, convert all units given to inches:

Length: feet $\rightarrow$ 180 inches

Width: feet $\rightarrow$ 120 inches

Then, find the area of the entire space you are covering. Since the space is rectangular (this can be assumed since only length and width are given as measurements), multiply the length and width to find the total area: 21,600 square inches.

Next, find the area of each of the tiles: $8 \times 8 = 64$ square inches. Divide the total area of the space by the area of each of your tiles: $21600 \div 64 = 337.5$ . In cases where you are covering a certain area with an object, always round up if you have a decimal (no matter how small), because you cannot simply buy $\tfrac{1}{2}$ of a tile.

The answer is 338 .

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Example Question #421 : Geometry

Vikram is looking at a scale drawing of a room he is building. The drawing is of a rectangle that measures inches by inches. If he knows the length of the longer side of the room will measure feet, what is the area of the room?

Possible Answers:

$400ft^{2}$

$600 ft^{2}$

$500 ft^{2}$

$650ft^{2}$

Correct answer:

$600 ft^{2}$

Explanation:

When solving such problems, always make sure that your units of measurement are all the same. In the case of this problem, you must convert feet to inches. Multiply 30 by 12 in order to get its equivalent in inches.

$30 \times 12 = 360$

We know that the 30 feet corresponds with the side of the drawing that is 18 inches because it is stated that the longest side will be 30 feet. Divide 360 by 18 in order to find the ratio of the actual size of the room to the measurements on the drawing

$360 \div 18 = 20$

This means that the actual measurements of the room are 20 times the measurements of the drawing. Multiply 20 times 12 in order to find the measurement of the shorter side in inches.

$20 \times 12 = 240$

Divide both the 360 and 240 by 12 to convert the measurements back into feet.

$360 \div 12 = 30$

$240 \div 12 = 20$

Then multiply the results to get the final answer.

$30ft \times 20 ft = 600ft^{2}$

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Example Question #1 : How To Find The Area Of A Quadrilateral

If a trapezoid has base lengths of $14\:cm$ and $18\:cm$ and a height of $7\:cm$ , what is its area?

Possible Answers:

$102\:cm^2$

$112\:cm^2$

$124\:cm^2$

$118\:cm^2$

Correct answer:

$112\:cm^2$

Explanation:

Use the formula for area of a trapezoid:

$A=\frac{(b_{1}+b_{2})(h)}{2}$

Where is the area, b_1 and b_2 are the lengths of the two bases, and is the height.

In this case:

$A=\frac{(14\:cm+18\:cm)(7\:cm)}{2}=112\:cm^2$

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Example Question #1 : How To Find The Area Of A Quadrilateral

A parallelogram has a side length of $15\:cm$ , a height of $12\:cm$ , and a base length of $20\:cm$ . What is its area?

Possible Answers:

$240\:cm^2$

$180\:cm^2$

$210\:cm^2$

$300\:cm^2$

Correct answer:

$240\:cm^2$

Explanation:

Use the formula for area of a parallelogram:

A=bh

Where is the area, is the base length, and is the height.

In this case:

$A=(20\:cm)(12\:cm)=240\:cm^2$

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ACT Math : How to find the area of a quadrilateral

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Area Of A Quadrilateral

Example Question #421 : Geometry

Example Question #1 : How To Find The Area Of A Quadrilateral

Example Question #1 : How To Find The Area Of A Quadrilateral

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