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Basic Geometry : How to find the area of a rectangle

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Example Questions

Example Question #201 : Quadrilaterals

Find the length of a diagonal of a square with side length 6.

Possible Answers:

$12\sqrt{2}$

$6\sqrt2$

Correct answer:

$6\sqrt2$

Explanation:

To find the diagonal of a square recall that the diagonal will create a triangle where the width and length are legs of the triangle and the diagonal is the hypotenuse.

To solve, simple use the Pythagorean Theorem and solve for the hypotenuse, which will be the diagonal of the square.

Thus,

$c=\sqrt{a^2+b^2}=\sqrt{6^2+6^2}=\sqrt{2*6^2}=6\sqrt2$

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Example Question #208 : Rectangles

A rectangle has length of $14\;cm$ and width that is one fourth the length. What would be the area of the rectangle rounded to the nearest tenth?

Possible Answers:

$56\;cm^2$

$42.7\;cm^2$

$17.5\;cm^2$

$49\;cm^2$

$38.8\;cm^2$

Correct answer:

$49\;cm^2$

Explanation:

To calculate the area, we first need to find the width of the rectangle. With the provided information, we can find the width as such:

$\frac{1}{4}\cdot14\;cm=3.5\;cm$

We can then solve for area:

$Area=3.5\;cm\cdot14\;cm=49\;cm^2$

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Example Question #616 : Basic Geometry

A rectangle has a width of $4\;cm$ and a diagonal of $8.3\;cm$ . Find the area of the rectangle, rounding all values to the nearest tenth.

Possible Answers:

$12.3\;cm^2$

$21.7\;cm^2$

$11.3\;cm^2$

$33.2\;cm^2$

$29.2\;cm^2$

Correct answer:

$29.2\;cm^2$

Explanation:

Before we can solve for area, we must first solve for the length of the rectangle. Since we have a value for width and the diagonal, we can use the Pythagorean Theorem:

$\\(8.3\;cm)^2=(4\;cm)^2+b^2\\68.9\;cm^2=16\;cm^2+b^2\\b^2=52.9\;cm^2\\b=\sqrt(52.9\;cm^2)\approx7.3\;cm$

Now that we have values for both length and width, we can calculate the area of the rectangle:

$7.3\;cm\cdot4\;cm=29.2\;cm^2$

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Example Question #617 : Basic Geometry

If Betty's barn with a width of $35\;ft$ and a length that is $32\;ft$ short of four times the width, what would be the area of the floor space of the barn?

Possible Answers:

$3,460\;ft^2$

$3,780\;ft^2$

$2,885\;ft^2$

$4,270\;ft^2$

$3,090\;ft^2$

Correct answer:

$3,780\;ft^2$

Explanation:

To find the area of the barn, we must first find the length. We can do this by using the given information to draft an algebraic equation:

$\\Length'=4(width')-32'\\L=4\cdot35'-32'\\L=140'-32'=108'$

Now that we know both the length and width, we can determine the area of the barn:

$Area=35\;ft\cdot108\;ft=3,780\;ft^2$

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Example Question #211 : Quadrilaterals

Find the area of a rectangle given length 7 and width 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a rectangle. Thus,

A=l*w=7*2=14

If you forget the formula, simply imagine you have two rows of blocks with 7 in them each. If you count the total number of blocks you have, you will realize you have 14!

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Example Question #619 : Basic Geometry

If the radius of the circle is , find the area of the shaded region of the rectangle.

Possible Answers:

201.32

202.28

209.46

208.64

Correct answer:

209.46

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(5)^2$

$\text{Area of circle}=25\pi$

Now, recall how to find the area of a rectangle.

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=12 \times 24$

$\text{Area of Rectangle} =288$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=288-25\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=209.46$

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Example Question #212 : Quadrilaterals

If the radius of the circle is , find the area of the shaded region of the rectangle.

Possible Answers:

398.74

365.21

336.90

373.24

Correct answer:

336.90

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(6)^2$

$\text{Area of circle}=36\pi$

Now, recall how to find the area of a rectangle.

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=15 \times 30$

$\text{Area of Rectangle}=450$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=450-36\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=336.90$

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Example Question #64 : How To Find The Area Of A Rectangle

If the radius of the circle is $\frac{2}{3}$ , what is the area of the shaded region of the rectangle?

Possible Answers:

17.50

16.33

16.98

16.60

Correct answer:

16.60

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times\left(\frac{2}{3}\right)^2$

$\text{Area of circle}=\frac{4}{9}\pi$

Now, recall how to find the area of a rectangle.

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=3\times 6$

$\text{Area of Rectangle}=18$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=18-\frac{4}{9}\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=16.60$

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Example Question #213 : Quadrilaterals

If the radius of the circle is 1.3 , what is the area of the shaded region of the rectangle?

Possible Answers:

21.69

20.54

21.99

20.79

Correct answer:

21.69

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(1.3)^2$

$\text{Area of circle}=1.69\pi$

Now, recall how to find the area of a rectangle.

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=3\times 9$

$\text{Area of Rectangle}=27$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=27-1.69\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=21.69$

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Example Question #214 : Quadrilaterals

If the radius of the circle is , what is the area of the shaded region of the rectangle?

Possible Answers:

32.43

31.02

33.69

37.15

Correct answer:

32.43

Explanation:

In order to find the area of the shaded region, we will need to subtract the area of the circle from the area of the rectangle.

Let's start by finding the area of a circle. Recall the formula to find the area of a circle:

$\text{Area of circle}=\pi\times\text{radius}^2$

Substitute in the value of the radius, which is given by the question.

$\text{Area of circle}=\pi\times(2)^2$

$\text{Area of circle}=4\pi$

Now, recall how to find the area of a rectangle.

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the values given by the figure to find the area of the rectangle.

$\text{Area of Rectangle}=5\times 9$

$\text{Area of Rectangle}=45$

Now, find the area of the shaded region.

$\text{Area of shaded region}=\text{Area of Rectangle}-\text{Area of Circle}$

$\text{Area of shaded region}=45-4\pi$

Solve and round to two decimal places.

$\text{Area of shaded region}=32.43$

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Basic Geometry : How to find the area of a rectangle

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #201 : Quadrilaterals

Example Question #208 : Rectangles

Example Question #616 : Basic Geometry

Example Question #617 : Basic Geometry

Example Question #211 : Quadrilaterals

Example Question #619 : Basic Geometry

Example Question #212 : Quadrilaterals

Example Question #64 : How To Find The Area Of A Rectangle

Example Question #213 : Quadrilaterals

Example Question #214 : Quadrilaterals

All Basic Geometry Resources

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