### All ISEE Middle Level Math Resources

## Example Questions

### Example Question #10 : Geometry

What is the area of a rectangle with length and width ?

**Possible Answers:**

**Correct answer:**

The formula for the area, , of a rectangle when we are given its length, , and width, , is .

To calculate this area, just multiply the two terms.

### Example Question #1 : Rectangles

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

**Possible Answers:**

**Correct answer:**

Figure A has area square inches.

Figure B has area square inches, 1 foot being equal to 12 inches.

Figure C has area square inches.

The figures, arranged from least area to greatest, are A, B, C.

### Example Question #2 : Rectangles

Give the surface area of the above box in square inches.

**Possible Answers:**

**Correct answer:**

Use the surface area formula, substituting :

square inches

### Example Question #1 : Area

**Possible Answers:**

**Correct answer:**

The area of a rectangle can be found by multiplying the length by the width.

### Example Question #4 : Rectangles

Give the area of the above rectangle in square feet.

**Possible Answers:**

**Correct answer:**

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

Use the area formula, substituting :

square feet

### Example Question #11 : 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?

**Possible Answers:**

**Correct answer:**

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 #6 : Rectangles

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?

**Possible Answers:**

**Correct answer:**

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 #7 : Rectangles

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

**Possible Answers:**

**Correct answer:**

Divide each dimension by 100 to convert centimeters to meters:

Multiply length by width:

square meters

### Example Question #8 : Rectangles

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.

**Possible Answers:**

**Correct answer:**

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 : Rectangles

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

**Possible Answers:**

**Correct answer:**

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

Multiply length by width:

square feet