4.2 Mensuration and Calculation

• What does mensuration involve measuring and calculating?

  Geometric properties
• Why is mensuration essential in various disciplines?

  Practical applications
• Match the shape with its area formula:

  Rectangle ↔️ Length × Width

  Triangle ↔️ ½ × Base × Height

  Circle ↔️ π × Radius²
• The perimeter of a circle is called its circumference.


  True
• Mensuration is only used in mathematics and has no practical applications in fields like engineering or architecture.

  False
• Mensuration is irrelevant for problem-solving in design and construction.

  False
• What is a rectangle defined as in mensuration?

  Four-sided shape with right angles
• What is the definition of mensuration in terms of geometric properties?

  Measuring and calculating
• Match the shape with its perimeter or circumference formula:

  Rectangle ↔️ 2 × (Length + Width)

  Triangle ↔️ Sum of all sides

  Circle ↔️ 2 × π × Radius
• What is the area formula for a triangle?

  ½ × Base × Height
• The area of a rectangle is calculated using the formula: Length × Width
• A rectangle with a length of 5 cm and a width of 3 cm has an area of 15 cm²
• What is the approximate area of a circle with a radius of 2.5 m?

  19.63 m²
• Why is mensuration considered a fundamental part of mathematics?

  Practical applications
• The circumference of a circle is its perimeter.


  True
• The perimeter of a triangle is calculated by adding the lengths of all its sides
• The perimeter of a triangle is the total length of its outer boundary.


  True
• The circumference of a circle is calculated using the formula 2 × π × Radius

  True
• What is the area of a rectangle with a length of 8 cm and a width of 5 cm?

  40 cm²
• The area of a shape must always be expressed in square units.

  True
• The volume of a cube with a side length of 5 cm is 125 cm³
• The volume of a cylinder with a radius of 2 m and a height of 5 m is approximately 62.83 m³
• The surface area of a cube with side length 5 cm is 150 cm².

  True
• Steps to calculate the diagonal of a rectangle using Pythagoras' theorem

  1️⃣ Identify the formula: \(a^2 + b^2 = c^2\)

  2️⃣ Substitute the length and width values into the formula

  3️⃣ Calculate the diagonal
• What is the formula for Pythagoras' theorem?

  $a^{2} +$$b^{2} =$$c^{2}$
• What is the length of the third side of a triangle with sides 3 m and 4 m?

  5 m
• What are the three key geometric properties measured in mensuration?

  Area, perimeter, circumference
• Steps to calculate the area of a rectangle

  1️⃣ Identify the length and width

  2️⃣ Multiply the length by the width

  3️⃣ State the area in square units
• Units must be consistent when calculating volume.


  True
• The volume of a cuboid with dimensions 6 cm × 4 cm × 3 cm is 72 cm³
• What does the surface area of a 3D shape refer to?

  Total area of outer surface
• The surface area of a cylinder with radius 3 m and height 5 m is approximately 150.8 m²
• What is the formula for Pythagoras' theorem?

  $a^{2} +$$b^{2} =$$c^{2}$
• Pythagoras' theorem is applicable to non-right-angled triangles.

  False
• Converting 1.5 cubic meters to cubic centimeters results in 1,500,000 cm³
• What is the area of a garden plot that is 12 m long and 8 m wide?

  96 m²
• Mensuration is the measurement and calculation of geometric properties
• The area of a 2D shape is the amount of space inside its boundaries
• A triangle is a three-sided shape
• Mensuration involves determining the area, volume, perimeter, and circumference