Measurement, Space & Statistics
Measurement and Geometry: Area, Perimeter, Angles and Shapes
Year 7
- ✓By the end of this lesson students will be able to calculate the perimeter of polygons.
- ✓By the end of this lesson students will be able to establish and use formulas for the area of rectangles and triangles to solve problems.
- ✓By the end of this lesson students will be able to identify and classify angles (acute, right, obtuse, straight, reflex, revolution).
- ✓By the end of this lesson students will be able to identify and use properties of angles on a straight line, angles at a point, and vertically opposite angles.
- ✓By the end of this lesson students will be able to identify and use properties of corresponding, alternate interior, and co-interior angles associated with parallel lines.
- ✓By the end of this lesson students will be able to classify triangles and quadrilaterals based on their properties.
Key concepts
The perimeter of a two-dimensional shape is the total distance around its boundary. It is found by adding the lengths of all its sides. Perimeter is measured in linear units (e.g., millimetres (mm), centimetres (cm), metres (m), kilometres (km)).
Area is the amount of two-dimensional space a surface covers. It is measured in square units (e.g., square millimetres (mm²), square centimetres (cm²), square metres (m²), square kilometres (km²)).
The area of a rectangle is found by multiplying its length by its width.
The area of a triangle is half the product of its base and its perpendicular height. The perpendicular height is the shortest distance from the base to the opposite vertex.
Angles are formed when two lines or rays meet at a common point called a vertex. They are measured in degrees (°).\n\n* **Acute Angle**: An angle between 0° and 90°.\n* **Right Angle**: An angle exactly 90° (often marked with a square symbol).\n* **Obtuse Angle**: An angle between 90° and 180°.\n* **Straight Angle**: An angle exactly 180° (forms a straight line).\n* **Reflex Angle**: An angle between 180° and 360°.\n* **Angle of Revolution (or Full Rotation)**: An angle exactly 360°.
When lines intersect or are parallel, specific relationships exist between the angles formed:\n\n* **Angles on a Straight Line**: Angles that form a straight line add up to 180°.\n* **Angles at a Point**: Angles around a central point add up to 360°.\n* **Vertically Opposite Angles**: When two straight lines intersect, the angles opposite each other are equal.\n* **Angles Associated with Parallel Lines**: When a transversal line intersects two parallel lines:\n * **Corresponding Angles**: Are in the same relative position at each intersection and are equal.\n * **Alternate Interior Angles**: Are on opposite sides of the transversal and between the parallel lines, and are equal.\n * **Co-interior Angles**: Are on the same side of the transversal and between the parallel lines, and add up to 180°.
Two-dimensional shapes (polygons) are classified by their number of sides and properties.\n\n* **Triangles (3 sides)**:\n * **Equilateral**: All three sides are equal, all three angles are 60°.\n * **Isosceles**: Two sides are equal, the angles opposite these sides are equal.\n * **Scalene**: All sides are different lengths, all angles are different.\n * **Right-angled**: Has one angle that is 90°.\n\n* **Quadrilaterals (4 sides)**:\n * **Square**: All sides equal, all angles 90°.\n * **Rectangle**: Opposite sides equal, all angles 90°.\n * **Rhombus**: All sides equal, opposite angles equal.\n * **Parallelogram**: Opposite sides parallel and equal, opposite angles equal.\n * **Trapezium**: At least one pair of parallel sides.\n * **Kite**: Two pairs of equal-length sides that are adjacent to each other.
Key facts to remember
- 1Perimeter is the distance around a shape, measured in linear units.
- 2Area is the amount of surface a shape covers, measured in square units.
- 3Area of a rectangle: A = l × w.
- 4Area of a triangle: A = ½ × b × h.
- 5Angles on a straight line sum to 180°.
- 6Angles at a point sum to 360°.
- 7Vertically opposite angles are equal.
- 8When parallel lines are cut by a transversal: corresponding angles are equal, alternate interior angles are equal, and co-interior angles sum to 180°.
- 9A right angle is exactly 90°.
Worked examples
Example 1
Calculate the perimeter and area of a rectangle with a length of 8 cm and a width of 5 cm.
Answer
Perimeter = 26 cm, Area = 40 cm²
Remember to use linear units for perimeter and square units for area.
Example 2
A triangle has a base of 10 m and a perpendicular height of 6 m. Calculate its area.
Answer
Area = 30 m²
Ensure you use the perpendicular height, not a slanted side length.
Example 3
In the diagram, line AB is parallel to line CD. A transversal line EF intersects them. If ∠EGB = 70°, find the measure of ∠GHD and ∠BGH.
Answer
∠GHD = 70°, ∠BGH = 110°
Always state the geometric reason for your calculations (e.g., 'corresponding angles are equal').
Common mistakes
- ✗Confusing perimeter and area, or using incorrect units (e.g., cm for area).
- ✗Not using the perpendicular height when calculating the area of a triangle.
- ✗Misidentifying angle relationships, especially with parallel lines (e.g., confusing corresponding with alternate interior).
- ✗Assuming a shape has properties it doesn't (e.g., assuming all sides of a quadrilateral are equal without explicit information).
- ✗Forgetting to include units in the final answer.
Exam tips
- ★Always read the question carefully to determine whether perimeter or area is required.
- ★Draw diagrams and label all known lengths and angles to help visualise the problem.
- ★Show all your working steps clearly, including the formula used, substitution, and calculation.
- ★Remember to include the correct units (e.g., cm, cm², degrees) in your final answer.
- ★When solving for unknown angles, always state the geometric reason for your steps (e.g., 'angles on a straight line').
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