### All SSAT Upper Level Math Resources

## Example Questions

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

Mark wants to seed his lawn, which measures 225 feet by 245 feet. The grass seed he wants to use gets 400 square feet of coverage to the pound; a fifty-pound bag sells for $45.00, and a ten-pound bag sells for $13.00. What is the least amount of money Mark should expect to spend on grass seed?

**Possible Answers:**

**Correct answer:**

The area of Mark's lawn is . The amount of grass seed he needs is pounds.

He has two options.

Option 1: he can buy three fifty-pound bags for

Option 2: he can buy two fifty-pound bags and four ten-pound bags for

The first option is the more economical.

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

The width and height of a rectangle are and , respectively. Give the area of the rectangle in terms of .

**Possible Answers:**

**Correct answer:**

The area of a rectangle is given by multiplying the width times the height. As a formula:

Where:

is the width and is the height. So we can get:

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

The base length of a parallelogram is equal to the side length of a square. The base length of the parallelogram is two times longer than its corresponding altitude. Compare the area of the parallelogram with the area of the square.

**Possible Answers:**

**Correct answer:**

The area of a parallelogram is given by:

Where is the base length and is the corresponding altitude. In this problem we have:

or

So the area of the parallelogram would be:

The area of a square is given by:

weher is the side length of a square. In this problem we have , so we can write:

Then:

or:

### Example Question #4 : How To Find The Area Of A Rectangle

How many squares with the side length of 2 inches can be fitted in a rectangle with the width of 10 inches and height of 4 inches?

**Possible Answers:**

**Correct answer:**

Solution 1:

We can divide the rectangle width and height by the square side length and multiply the results:

rectangle width square length =

rectangle heightsquare length =

Solution 2:

As the results of the division of rectangle width and height by the square length are integers and do not have a residual, we can say that the squares can be perfectly fitted in the rectangle. Now in order to find the number of squares we can divide the rectangle area by the square area:

Rectangle area = square inches

Square area = square inches

So we can get:

### Example Question #5 : How To Find The Area Of A Rectangle

A rectangle has the area of 80 square inches. The width of the rectangle is 2 inches longer that its height. Give the height of the rectangle.

**Possible Answers:**

**Correct answer:**

The area of a rectangle is given by multiplying the width times the height. That means:

where:

width and height.

We know that: . Substitube the in the area formula:

Now we should solve the equation for :

The equation has two answers, one positive and one negative . As the length is always positive, the correct answer is inches.

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

A rectangle with a width of 6 inches has an area of 48 square inches. Give the sum of the lengths of the rectangle's diagonals.

**Possible Answers:**

**Correct answer:**

A rectangle has two congruent diagonals. A diagonal of a rectangle divides it into two identical right triangles. The diagonal of the rectangle is the hypotenuse of these triangles. We can use the Pythagorean Theorem to find the length of the diagonal if we know the width and height of the rectangle.

where:

is the width of the rectangle

is the height of the rectangle

First, we find the height of the rectangle:

So we can write:

inches

As a rectangle has two diagonals with the same length, the sum of the diagonals is inches.

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

A rectangle has the width of and the diagonal length of . Give the area of the rectangle in terms of .

**Possible Answers:**

**Correct answer:**

First we need to find the height of the rectangle. Since the width and the diagonal lengths are known, we can use the Pythagorean Theorem to find the height of the rectangle:

So we have:

So we can get:

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

The perimeter of a rectangle is 800 inches. The width of the rectangle is 60% of its length. What is the area of the rectangle?

**Possible Answers:**

**Correct answer:**

Let be the length of the rectangle. Then its width is 60% of this, or . The perimeter is the sum of the lengths of its sides, or

; we set this equal to 800 inches and solve for :

The width is therefore

.

The product of the length and width is the area:

square inches.

### Example Question #41 : Area Of Polygons

Rectangle A has length 40 inches and height 24 inches. Rectangle B has length 30 inches and height 28 inches. Rectangle C has length 72 inches, and its area is the mean of the areas of the other two rectangles. What is the height of Rectangle C?

**Possible Answers:**

**Correct answer:**

The area of a rectangle is the product of the length and its height, Rectangle A has area square inches; Rectangle B has area square inches.

The area of Rectangle C is the mean of these areas, or

square inches, so its height is this area divided by its length:

inches.

### Example Question #2 : How To Find The Area Of A Rectangle

The area of a rectangle is square feet. The width of the rectangle is four-sevenths of its length. Give the length of the rectangle in inches in terms of .

**Possible Answers:**

**Correct answer:**

Let be the length in feet. Then the width of the rectangle in feet is four-sevenths of this, or . The area is equal to the product of the length and the width, so set up this equation and solve for :

Since this is the length in feet, we multiply this by 12 to get the length in inches:

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