Perimeter And Area

1. What is the area of the figure?

4

8

2

The area of the figure is 8 because the figure is a rectangle with a length of 4 units and a width of 2 units. To find the area of a rectangle, you multiply the length by the width, which in this case is 4 x 2 = 8.

Explanation

The area of the figure is 8 because the figure is a rectangle with a length of 4 units and a width of 2 units. To find the area of a rectangle, you multiply the length by the width, which in this case is 4 x 2 = 8.

2. Which number sentence represents the area of the figure?

2 + 4 =

4 + 4 =

4 x 2 =

The number sentence 4 x 2 = represents the area of the figure.

Explanation

The number sentence 4 x 2 = represents the area of the figure.

3. Understanding area and perimeter can help me to know what it will cost me to put a new floor in my home or put a fence around my yard.

True

False

Understanding area and perimeter is important because it allows me to calculate the amount of material I will need for a project such as putting a new floor in my home or installing a fence around my yard. By knowing the area, I can determine the amount of flooring or fencing material required, which in turn helps me estimate the cost of the project accurately. Therefore, the statement is true.

Explanation

Understanding area and perimeter is important because it allows me to calculate the amount of material I will need for a project such as putting a new floor in my home or installing a fence around my yard. By knowing the area, I can determine the amount of flooring or fencing material required, which in turn helps me estimate the cost of the project accurately. Therefore, the statement is true.

4. For which figure would the perimeter be solved by the number sentence 4+6+4+6?

a.

b.

c.

Figure a

Figure b

Figure c

Figure c would have a perimeter that is solved by the number sentence 4+6+4+6 because it has sides of length 4 and 6. The perimeter of a figure is the sum of the lengths of all its sides, so adding up the lengths of the sides in figure c gives us a perimeter of 20.

Explanation

Figure c would have a perimeter that is solved by the number sentence 4+6+4+6 because it has sides of length 4 and 6. The perimeter of a figure is the sum of the lengths of all its sides, so adding up the lengths of the sides in figure c gives us a perimeter of 20.

5. Which figure has an area of 5? a.

b.

c.

A

B

C

Explanation

6. Which number sentence represents the area of the figure?

3 + 6 =

3 x 6 =

3 + 6 + 3 + 6 =

The number sentence "3 x 6 =" represents the area of the figure because it is a multiplication equation, and the area of a figure is calculated by multiplying the length by the width. In this case, the length is 3 and the width is 6, so multiplying them together gives us the area of the figure.

Explanation

The number sentence "3 x 6 =" represents the area of the figure because it is a multiplication equation, and the area of a figure is calculated by multiplying the length by the width. In this case, the length is 3 and the width is 6, so multiplying them together gives us the area of the figure.

7. Which number sentence represents the perimeter of the figure?

4+6+4+6 =

4 + 6 =

6 x 4 =

The given number sentence, 4+6+4+6, represents the perimeter of the figure.

Explanation

The given number sentence, 4+6+4+6, represents the perimeter of the figure.

8. A rectangle has a length of 8 meters and a width of 5 meters. What is its perimeter and area?

Perimeter: 26 meters, Area: 40 square meters

Perimeter: 26 meters, Area: 30 square meters

Perimeter: 40 meters, Area: 26 square meters

Perimeter: 30 meters, Area: 40 square meters

To find the perimeter and area of a rectangle with a length of 8 meters and a width of 5 meters:

The perimeter is calculated by adding the length and the width, then multiplying by 2. So, (8 + 5) times 2 equals 26 meters.

The area is calculated by multiplying the length by the width. So, 8 times 5 equals 40 square meters.

Therefore, the correct answer is: Perimeter: 26 meters, Area: 40 square meters

Explanation

To find the perimeter and area of a rectangle with a length of 8 meters and a width of 5 meters:

The perimeter is calculated by adding the length and the width, then multiplying by 2. So, (8 + 5) times 2 equals 26 meters.

The area is calculated by multiplying the length by the width. So, 8 times 5 equals 40 square meters.

Therefore, the correct answer is: Perimeter: 26 meters, Area: 40 square meters

9. A rectangle has a perimeter of 26 cm and an area of 40 cm². What is the difference between the length and width of the rectangle?

2 cm

3 cm

5 cm

6 cm

Let the length of the rectangle be 'l' and the width be 'w'. We are given:

Perimeter: 2(l + w) = 26 cm, which simplifies to l + w = 13 cm

Area: l * w = 40 cm²

We need to find the difference between the length and width, i.e., |l - w|.

To solve this, we can use the fact that (l + w)² - 4lw = (l - w)².

Substituting the given values: 13² - 4 * 40 = (l - w)² This simplifies to 169 - 160 = (l - w)² Therefore, 9 = (l - w)² Taking the square root of both sides, we get |l - w| = 3 cm.

Explanation

Let the length of the rectangle be 'l' and the width be 'w'. We are given:

Perimeter: 2(l + w) = 26 cm, which simplifies to l + w = 13 cm

Area: l * w = 40 cm²

We need to find the difference between the length and width, i.e., |l - w|.

To solve this, we can use the fact that (l + w)² - 4lw = (l - w)².

Substituting the given values: 13² - 4 * 40 = (l - w)² This simplifies to 169 - 160 = (l - w)² Therefore, 9 = (l - w)² Taking the square root of both sides, we get |l - w| = 3 cm.

10. Considering a single cube is a unit, what will be the perimeter of a rectangle formed by eight such cubes?

12

4

4 x 2

If a single cube has a unit area (which means each face of the cube has a side length of 1 unit), and you arrange 8 of these cubes to form a rectangular shape, it would be a 2x2x2 cube.

To find the perimeter of this rectangular shape, you can add up the lengths of all the edges. In this case, the perimeter would be:

Perimeter = 2 * (length + width + height)

Perimeter = 2 * (2 + 2 + 2)

Perimeter = 2 * 6

Perimeter = 12 units

So, the perimeter of the rectangle formed by 8 such cubes would be 12 units.

Explanation

If a single cube has a unit area (which means each face of the cube has a side length of 1 unit), and you arrange 8 of these cubes to form a rectangular shape, it would be a 2x2x2 cube.

To find the perimeter of this rectangular shape, you can add up the lengths of all the edges. In this case, the perimeter would be:

Perimeter = 2 * (length + width + height)

Perimeter = 2 * (2 + 2 + 2)

Perimeter = 2 * 6

Perimeter = 12 units

So, the perimeter of the rectangle formed by 8 such cubes would be 12 units.