Area and Perimeter Review

Calculate the area of a rectangle with length 5 units and width 3 units.

• 12 square units

• 15 square units

• 8 square units

• 10 square units

Answer explanation

To calculate the area of a rectangle, multiply the length by the width. In this case, 5 units * 3 units = 15 square units. Therefore, the correct answer is 15 square units.

Find the perimeter of a square with side length 7 units.

• 14 units

• 28 units

• 49 units

• 35 units

Answer explanation

The perimeter of a square is calculated by multiplying the side length by 4. Therefore, the perimeter of a square with a side length of 7 units is 7 * 4 = 28 units. Hence, the correct answer is 28 units.

Determine the composite area of a shape composed of a rectangle with dimensions 4 units by 6 units and a square with side length 5 units.

• 30 square units

• 60 square units

• 40 square units

• 49 square units

Answer explanation

The composite area is calculated by adding the area of the rectangle (4*6=24 square units) and the area of the square (5*5=25 square units) to get a total of 49 square units.

Calculate the area of a shaded region in a figure where a circle with radius 4 units is inscribed in a square.

• 16π square units

• 8π square units

• 12 square units

• 32 square units

Answer explanation

The area of the shaded region is the area of the square minus the area of the inscribed circle. Area = (side length)^2 - π(radius)^2 = 16 - 16π = 16π square units

Find the area of a regular hexagon with a side length of 8 units.

• 120√3 square units

• 64√3 square units

• 256 square units

• 192√3 square units

Answer explanation

The area of a regular hexagon can be calculated using the formula: (3√3 * side length^2) / 2. Substituting the side length of 8 units gives: (3√3 * 8^2) / 2 = 192√3 square units.

If the side length of a square is doubled, how does the area change?

• The area decreases by a factor of 2.

• The area increases by a factor of 2.

• The area increases by a factor of 4.

• The area remains the same.

Answer explanation

When the side length of a square is doubled, the area increases by a factor of 4 because the area is proportional to the square of the side length.

Henry is building a triangular garden fence with side lengths 5 units, 7 units, and 9 units. Calculate the perimeter of the garden fence.

• 15 units

• 24 units

• 21 units

• 18 units

Determine the composite area of a shape composed of a triangle with base 6 units and height 8 units and a rectangle with dimensions 5 units by 10 units.

• 48 square units

• 60 square units

• 74 square units

• 35 square units

Calculate the area of the shaded region where a colored circle with radius 4 units is perfectly placed inside a square.

• 18.4

• 50.24

• 12.56

• 3.14

Calculate the area of a regular octagon with a side length of 12 units.

• 312 square units

• 692.736 square units

• 144 square units

• 576 square units

Answer explanation

To find the area of a regular octagon, use the formula: Area = 2 * (1 + √2) * side length^2. Substituting the values, Area = 2 * (1 + √2) * 12^2 = 692.736 square units.