4.2 Mensuration and Calculation

• Area is a 2-dimensional measurement, while volume is a 3-dimensional measurement.


  True
• Mensuration allows us to quantify and analyze the physical world around us, making it a fundamental part of mathematics
• The volume of a sphere is calculated using the formula V = \frac{4}{3}\pi r^{3}</latex>.


  True
• The area of a triangle is calculated using the formula $A =$$\frac{1}{2}bh$, where *h* is the height
• The area of a triangle is given by $\frac{1}{2}bh$ where *b* is the base and *h* is the height.


  True
• Mensuration refers to the measurement and calculation of geometric properties
• What is measured by the length formula in mensuration?

  Line segment, side of a polygon
• What are the two distinct geometric properties measured in mensuration?

  Area and volume
• Match the key aspect of mensuration with its description:

  Definition ↔️ The measurement and calculation of geometric properties

  Purpose ↔️ Quantify and analyze the physical world

  Applications ↔️ Construction, engineering, navigation, resource management
• The area of a triangle is calculated using the formula $A =$$\frac{1}{2}bh$, where *b* is the base
• The area of a circle is calculated using the formula $A =$$\pi r^{2}$.


  True
• The area of a rectangle is calculated using the formula lw
• What is the formula for the area of a circle?

  $A =$$\pi r^{2}$
• Arrange the key aspects of mensuration in a logical order:

  1️⃣ Definition: The measurement and calculation of geometric properties

  2️⃣ Purpose: Quantify and analyze the physical world

  3️⃣ Applications: Construction, engineering, navigation, resource management
• The volume of a sphere is given by the formula $V =$$\frac{4}{3}\pi r^{3}$.


  True
• The perimeter of a triangle is calculated by summing the lengths of all its sides.

  True
• Volume refers to the amount of space
• Mensuration involves the measurement and calculation of geometric properties.


  True
• Match the geometric property with its example formula:

  Area ↔️ A = \pi r^{2}</latex>

  Volume ↔️ $V =$$lwh$

  Perimeter ↔️ Sum of all side lengths
• What is the formula for the area of a triangle?

  $A =$$\frac{1}{2}bh$
• What does area measure in geometric terms?

  The surface of a shape
• What type of dimensions does volume measure?

  3-dimensional
• What is the area of a rectangle with length 5 units and width 3 units?

  15 square units
• Mensuration refers to the measurement and calculation of the geometric properties of shapes and objects, such as their length, area, volume, and perimeter
• Order the following geometric properties from least to most dimensions:

  1️⃣ Length

  2️⃣ Perimeter

  3️⃣ Area

  4️⃣ Volume
• A sheet of paper has area but no volume.


  True
• Mensuration has applications in fields such as construction, engineering, and navigation.


  True
• The perimeter of a polygon is the sum of all its side lengths.
• Area measures the surface of a 2D shape, while volume measures the space occupied by a 3D object.


  True
• What is the area of a rectangle with a length of 5 units and a width of 3 units?

  15 square units
• The volume of a rectangular prism is calculated using the formula $V =$$lwh$
• Surface area refers to the total area of the outer surface
• Order the geometric properties from least to most complex to measure:

  1️⃣ Length

  2️⃣ Perimeter

  3️⃣ Area

  4️⃣ Volume
• Match the property with its description:

  Area ↔️ 2-dimensional measurement

  Volume ↔️ 3-dimensional measurement
• Geometric formulas are essential for practical applications in fields like construction and engineering.

  True
• The area of a rectangle is calculated as length times width.
• Match the shape with its area formula:

  Rectangle ↔️ $A =$$lw$

  Triangle ↔️ $A =$$\frac{1}{2}bh$

  Circle ↔️ $A =$$\pi r^{2}$
• Knowing the area of 2D shapes is crucial for calculating material coverage.


  True
• Match the 3D shape with its volume formula:

  Cube ↔️ $V =$$s^{3}$

  Rectangular Prism ↔️ $V =$$lwh$

  Sphere ↔️ $V =$$\frac{4}{3}\pi r^{3}$

  Cylinder ↔️ $V =$$\pi r^{2} h$
• Knowing the surface area of 3D shapes is important for calculating material needed to cover an object.


  True