SSAT Middle Level Math : Geometry

Example Questions

Example Question #161 : Geometry

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation:

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is .

The perimeter of the first square is  , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

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

The following question is about the Jones family wanting to buy square foot tiles for their rectangular basement. Their basement perimeter is 74 feet, with one of the sides being 15 feet long.

How many square foot titles are the Jones family needing to purchase in order to tile their basement?

Explanation:

From the given information we know that the perimeter of the rectangular basement is 74 feet. We also know that one side of the rectangular basement is 15 feet. This means that the opposite side is also 15 feet long because the equivalent opposite sides rule of rectangles. In order to find the lengths of our other two sides of the rectangle, we need to subtract our two 15 feet sides from the perimeters 74 feet.

.

We know that the last two sides have to add up to 44 feet. Since the rules of rectangles say opposite sides are equivalent, we must take 44 feet and divide by the 2 sides. So 44 divided by 2 is 22 feet, meaning each side must be 22 feet. After adding up all the sides we can confirm that our perimeter is 74 feet.

Now we know all the sides of the rectangle, we are able to move to the next step, finding the area. We must find the area, because the tiles are square feet. So in order to find the area we must take the length of the rectangle and multiply it to the width.

Knowing the area of the rectangular basement we also know how many tile are needed to fill the basement for the Jones family. It is exactly 330 square feet tile needed.

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

Which of the following is equal to the area of a rectangle with length 250 centimeters and width 140 centimeters?

Explanation:

Divide each dimension by 100 to convert centimeters to meters:

Multiply length by width:

square meters

Example Question #8 : How To Find The Area Of A Rectangle

A hectare is a unit of area equal to 10,000 square meters.

A rectangular plot of land measures 1,400 meters by 800 meters. Give the area of this plot in hectares.

Explanation:

Multiply length times width to get the area in square meters:

square meters

Divide by 10,000 to convert to hectares:

hectares

Example Question #9 : How To Find The Area Of A Rectangle

Which of the following is equal to the area of a rectangle with length 27 inches and width 15 inches?

Explanation:

Divide each dimension by 12 to convert from inches to feet:

Multiply length by width:

square feet

Example Question #1991 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Which of the following is equal to the area of a rectangle with length  feet and width  feet?

Explanation:

Multiply each dimension by 12 to convert from feet to inches:

Now multiply this length and width to get the area:

Example Question #12 : How To Find The Area Of A Rectangle

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its surface area in square feet.

Explanation:

Divide each dimension in inches by 12 to convert from inches to feet:

feet

feet

feet

Now, substitute in the surface area formula:

The area of a rectangle with a length of and a width of is . Find .

Explanation:

The area of a rectangle is the product of length and width:

Give the area of a rectangle with a length of and a width of .

Explanation:

We know that:

where:

So we can write:

Example Question #141 : Geometry

A rectangular table has a length of  and a width of . Give the area of the table.

Explanation:

We know that:

where:

So we can write: