To calculate the area of a triangle use the formula:
Area = One half multiplied by the base multiplied by the height (A=1/2 x bh)
National Curriculum Standards: Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms.
To calculate the volume of any prism, multiply the area of the base by the height (or in the case above, the trapezium by the length of the trailer). Make sure all the units are the same before starting your calculations.
National Curriculum Standard: “Students use formulas for the area and perimeter of rectangles.”
The perimeter of a rectangle is calculated by adding the four sides. The area of a rectangle is calculated by multiplying the length by the width.
Perimeter =2 x (L+W) = 2L + 2W
Area = Length x Width = LW
Find at least three rectangles around the classroom and measure the length and width. Draw a sketch showing the object and the measurements, including the units (millimetres, centimetres or metres). Calculate the perimeter and the area of the object using the formulae above.
For example; your laptop, the table top, your maths book, a window pane, the door, the whiteboard, the front of the heater, the noticeboard etc.
The perimeter of the locker door will be:
(2 x 35) + (2 x 59) = 70 + 118 = 188 cm
The area of the locker door will be:
35 x 59 = 2065 cm^2 (square centimetres)
This term we will be studying Measurement and Geometry.
Year 7 Maths (JacPlus Chapter 9 – Measurement and Chapter 5 – Geometry)
By the end of this term I hope you will be able to:
- Use appropriate units of measurement
- Calculate the perimeter of 2D shapes
- Calculate the area of triangles, quadrilaterals and composite shapes.
- Identify types of polygons (different triangles and quadrilaterals)
- Estimate, measure and draw angles between 0 and 360 degrees.
- Identify the properties of parallel and perpendicular lines and the angles that form between them.
- Calculate the missing angles in polygons, knowing that the internal angles of a triangle add to 180 degrees.
- Recognise various transformations (translations, reflections, rotations and dilations)
Year 8 Maths (JacPlus Chapter 7 – Congruence and Chapter 10 – Measurement)
By the end of this term I hope you will be able to:
- Use and convert units of measurement for perimeter, area and volume
- Calculate the area of various quadrilaterals.
- Calculate the area and perimeter of circles.
- Calculate the volume of various prisms using formulae.
- Identify congruent shapes
- Transform various shapes (translate, dilate, rotate and reflect).
- Solve geometric problems using congruence.
- Work out problems around different time zones using the 24 hour clock.
Learning Intention: Students will understand how to calculate the area of a triangle, using the rule Area = 1/2 x base x height.
Success Criteria: Students will draw and label at least four different triangles of the same area.
How many different triangles can you draw with an area of 120 cm sq? Use graph paper, where 1 cm ~ 10 cm and label the base and the height, showing any right angles.
Learning Intention: “Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving. Recognise and solve problems involving simple ratios.”
Success Criteria: Students will be able to calculate the area of various 2D shapes, including triangles, squares, rectangles and composites of these shapes. They will draw a house plan to scale and calculate the floor area of the house.
Homework: Measure the length and width of your bedroom and one other room in your house in meters. Notice that your doorways are about 1.0 meter wide.
Today’s task is to draw a scale plan of a holiday house. A rough estimate of the cost to construct a home is at least $1,000 per square meter. Your budget is $250,000, so the house must be less than 250 square meters in area. Use a scale – 1.0m to 1.0cm is a good way to start. So, 1.0cm on the plan, represents 100cm (1.0m) on the ground. Your scale is 1:100. Your holiday house should include the following rooms:
- Lounge/Living area
- 2 Bedrooms
Learning Intention: To understand how to calculate the area of a triangle and why the formula (A = 1/2 x base x height) works for all triangles.
Success Criteria: Students will complete the interactive “Area of Triangles” activity with at least 80% of answers correct.
1. Classify triangles according to their side and angle properties and describe quadrilaterals.
2. Establish the formulas for areas of triangles, rectangles and parallelograms and use these in problem solving.
3. Demonstrate that the angle sum of a triangle is 180 degrees and use this to find the angle sum of a quadrilateral.
This is Nick’s place. He has shown all the measurements in the correct units and calculated the area of the paralellogram with the correct formulae. Great work!
Learning Intention: Understand that the area of all composite shapes can be calculated by breaking the shape down into known areas.
Success Criteria: You will be able to summarize the formulae to calculate the area of the following 2 dimensional shapes and break down a composite shape by identifying each of the known shapes and correctly calculating their area.
- squares and rectangles
- circles and annuli
Some examples of these kinds of problems are in Exercise 8G (page 326) of MathsQuest8. Here are some other activities to learn about the area of composite shapes.
- An L-shaped room has a perimeter of 20m. What might the area of the floor be?
- The difference in areas of two rectangles is 32cm (squared). What might the widths and lengths of the two rectangles be?
Your homework (due Friday) is one of the following:
- Use Google Maps or Google Earth to find an aerial view of an unusual shape, take a screen shot and calculate it’s area using the scale measurements. Copy your screen shot into “Paint”, add the measurements, calculate the area and email it to me. You may choose a large building, carpark or arena (the MCG or Etihad stadium for example) or perhaps your farm or property.
- Use a stencil or simple font to write the initials of your name, and calculate the area of the letters. Make sure you email me a copy of your calculations, or leave a comment below about your task.