Mathematics - Term 1 - Week 7

Geometry is a branch of mathematics that deals with shapes, sizes, and the properties of space. In this lesson, we will focus on two-dimensional shapes such as triangles, quadrilaterals, and circles. Each shape has unique properties; for example, a triangle has three sides and three angles, while a quadrilateral has four sides and can be classified into various types such as squares, rectangles, and trapezoids. Understanding these properties helps us in solving real-world problems.

To find the area of a triangle, we use the formula: Area = 1/2 × base × height. For example, if a triangle has a base of 10 cm and a height of 5 cm, we can calculate the area as follows: Area = 1/2 × 10 cm × 5 cm = 25 cm². This example illustrates how to apply the formula and the importance of identifying the base and height correctly.

Let's work together to identify different types of quadrilaterals. I will show you several shapes, and you will classify them as squares, rectangles, rhombuses, or trapezoids based on their properties. Remember, a square has all sides equal and all angles right angles, while a rectangle has opposite sides equal and all angles right angles. A rhombus has all sides equal but angles are not necessarily right angles, and a trapezoid has at least one pair of parallel sides.

Now it's your turn! Solve the following problems independently: 1) Calculate the area of a rectangle with a length of 8 cm and a width of 3 cm. 2) Find the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 9 cm. Show all your working clearly. This practice will help reinforce your understanding of area and perimeter calculations.

• 90 degrees
• 180 degrees
• 360 degrees
• 270 degrees

Answer: 180 degrees

The sum of the interior angles of any triangle is always 180 degrees.

• Opposite sides are equal
• All sides are equal
• All angles are right angles
• All of the above

Answer: All of the above

A square has all sides equal and all angles are right angles, making all these properties true.

Answer: A parallelogram is a four-sided figure (quadrilateral) where opposite sides are parallel and equal in length.

This definition captures the essential characteristics of a parallelogram.

• 40 cm²
• 50 cm²
• 60 cm²
• 30 cm²

Answer: 40 cm²

Area is calculated as length × width, so 10 cm × 4 cm = 40 cm².

Answer: 24 cm

Perimeter is the sum of all sides: 6 cm + 8 cm + 10 cm = 24 cm.

• Square
• Rectangle
• Trapezoid
• Rhombus

Answer: Trapezoid

A trapezoid is defined as having at least one pair of parallel sides.

• 30 cm²
• 60 cm²
• 24 cm²
• 36 cm²

Answer: 30 cm²

Using the area formula for triangles: Area = 1/2 × base × height = 1/2 × 12 cm × 5 cm = 30 cm².