4.2 Mensuration and Calculation

• What are the two main properties of 2D shapes that are commonly calculated using formulas?

  Area and perimeter
• The area of a rectangle is calculated using the formula Length x Width
• What is the formula for the perimeter of a triangle?

  Sum of all side lengths
• The area of a circle is calculated using the formula \pi r^{2}</latex>
• What is the formula for the perimeter of a square?

  4 x Side
• The formulas for 2D shapes are essential for determining their size and boundary.
• Match the 3D shape with its surface area formula:

  1️⃣ Cube ||| 6 x Side^2

  2️⃣ Sphere ||| $4\pi r^{2}$

  3️⃣ Cylinder ||| $2\pi r^{2} +$$2\pi rh$

  4️⃣ Rectangular Prism ||| 2 x (Length x Width + Length x Height + Width x Height)
• What is the formula for the volume of a cube?

  Side^3
• The surface area of a sphere is calculated using the formula $4\pi r^{2}$
• What is the formula for the volume of a cylinder?

  $\pi r^{2}h$
• 3D shape formulas allow you to calculate their volume and surface area.
• What is the area of a rectangle with a length of 12 cm and a width of 8 cm?

  96 cm^2
• The perimeter of a circle with a radius of 5 cm is approximately $10\pi$
• What is the perimeter of a square with a side length of 7 cm?

  28 cm
• What is the formula for the area of a rectangle?

  Length x Width
• The area of a circle is calculated using the formula $\pi r^{2}$
• What is the formula for the perimeter of a square?

  4 x Side
• The area of a 2D shape represents its size, while the perimeter represents its boundary.
• What is the formula for the perimeter of a rectangle?

  2 x (Length + Width)
• The circumference of a circle is calculated using the formula $2\pi r$
• What is the formula for the area of a square?

  Side x Side
• Calculating the area and perimeter of 2D shapes is essential for solving geometry problems.
• What is the surface area formula for a cube?

  $6 \times \text{Side}^{2}$
• The surface area of a cylinder is calculated using the formula 2\pi r^{2} + 2\pi rh</latex>
• What is the volume formula for a rectangular prism?

  $\text{Length} \times \text{Width} \times \text{Height}$
• Surface area is the measure of the outer boundary of a 3D object.
• What is the area of a rectangle with length 12 cm and width 8 cm?

  96 cm^2
• The perimeter of a triangle with side lengths 10 cm, 8 cm, and 14 cm is 32 cm
• What is the perimeter of a square with side length 7 cm?

  28 cm
• The area of a circle with radius 5 cm is $25\pi$ cm^2.
• What is the area of a rectangle with length 12 cm and width 8 cm?

  96 cm^2
• The surface area of a cube with side length 5 cm is 150 \text{ cm}^{2}</latex>
• What is the volume of a sphere with radius 3 cm?

  $36\pi \text{ cm}^{3}$
• What is the surface area of a cylinder with radius 4 cm and height 10 cm?

  $112\pi \text{ cm}^{2}$
• Calculating the volume of 3D shapes involves the same formulas as calculating the area of 2D shapes.

  False
• What properties of 3D objects can be calculated using the formulas provided?

  Volume and surface area
• The surface area and volume of a sphere are always equal when the radius is 3 cm.
• Match the 2D shape with its area formula:

  Rectangle ↔️ Length x Width

  Triangle ↔️ 1/2 x Base x Height

  Circle ↔️ $\pi r^{2}$

  Square ↔️ Side x Side
• Steps to practice calculating the surface area and volume of 3D shapes

  1️⃣ Identify the Shape

  2️⃣ Recall the Formula

  3️⃣ Apply the Formula
• What is the surface area of a cube with a side length of 5 cm?

  150 cm^2