Area of Quadrilaterals Mathematics Area of Quadrilaterals

Lesson Objectives The aim of this powerpoint is to help you… calculate the area of parallelograms calculate the area of kites calculate the area of trapezia

Area Area is the amount inside a 2D (flat) shape. REMINDER: Area is the amount inside a 2D (flat) shape. Area is calculated by multiplying 2 perpendicular dimensions (distances) together The unit types must be the same before multiplying and therefore result in square units

Quadrilaterals Quadrilaterals are 4-sided shapes They include… rectangles; squares (special types of rectangles); parallelograms; rhombuses (special types of parallelograms); trapezia; kites; deltas (which you don’t need to learn). You should know: Area of a rectangle = length × width

Parallelograms A parallelogram is like a tilted rectangle BUT you do NOT multiply the longer side by the shorter side as these are NOT perpendicular to each other! However, if we cut one corner off and put it at the other end, we can make a rectangle. The area of the parallelogram which is now a rectangle has not changed, but now we can calculate the area!

Area Formula for Parallelogram The length of the rectangle formed is the base of the original parallelogram The width of the rectangle formed is the perpendicular height of the parallelogram (NOT the slanting side!) The area of this new rectangle, and therefore the area of the parallelogram is: base × perpendicular height slant perp. height base perp. height slant base

Quick Practice Calculate the area of this parallelogram… 6cm 4.5cm 8cm Area = base × perp. height So Area = 8cm × 4.5cm = 36cm²

What next? Print out the notes called PAV2b-AreaQ. Read through them and make sure you answer any questions on the areas of parallelograms. Work through the MyMaths lesson and its online homework called Area of a Parallelogram found at: http://app.mymaths.co.uk/267-resource/area-of-a-parallelogram http://app.mymaths.co.uk/267-homework/area-of-a-parallelogram Save and complete the worksheet called AreaP-S1.xlsx Now continue to work through this powerpoint

Kites The diagonals in a kite run vertically and horizontally so they are perpendicular Look at the diagram again We can re-arrange a kite into a rectangle shape The length and width of the rectangle are the longer diagonal and ½ of the shorter diagonal of the original kite.

Area Formula for a Kite Therefore the area of a kite is its diagonals multiplied together then divided by 2 i.e. A = ½ of d1 × d2 long diagonal ½ of the short diagonal

Quick Practice Calculate the area of this kite… 8.5m 10m 13m 19m Area = ½ of diagonal 1 × diagonal 2 So Area = ½ of (19 × 10) = ½ of 190 = 95m²

Squares & Rhombuses You can use the formula for the area of a rectangle for finding the area of a square. You can use the formula for the area of a parallelogram for finding the area of a rhombus. However, the diagonals of a square and of a rhombus cross at 90° so you can use the formula for calculating the area of a kite for them too! Area = length × width Area = base × p.height Area = ½ of diagonal 1 × diagonal 2

Formula Triangles Remember that multiplication and division are directly linked, so if two numbers are multiplied together to give a value, then that value divided by either of the original numbers gets you back to the other original number. Formula triangles write the multiplied values on the bottom and their product on the top. You then cover up the item you want, to find the formula for the other two items. Area of a Parallelogram = base x perp height (A = bh) Here is it’s formula triangle: If you wish to find the base, cover ‘b’… You now see that b = A/h i.e. Area divided by the perpendicular height. A b h

Trapezia A trapezium can also be made into a rectangle as shown The length of rectangle made is halfway between the length of the top of the trapezium and the length of the bottom of the trapezium (i.e. average length) The width of the new rectangle is the perpendicular height of the trapezium. top ph bottom average length perp. height perp. height

Area Formula for a Trapezium To find the average of two numbers you add them together and divide their total by 2. The average length is therefore HALF of the total of the two parallel sides added together. This average length is then multiplied by the perpendicular height. Formula: A = ½(a + b)h b a h

Quick Practice Calculate the area of this trapezium… Check by splitting the shape into a triangle on top of a rectangle… Triangle = ½ of 4 x 12 = 24 Rectangle = 11 x 12 = 132 Total = 24 + 132 = 156 P Calculate the area of this trapezium… 15cm 11cm 12.4cm 12cm Area = ½ of (15 + 11) × 12 So Area = ½ of 26 × 12 = 13 × 12 = 156cm²

What next? Finish reading through the notes, making sure you answer any questions on the areas of other quadrilaterals. Work through the MyMaths lesson and its online homework called Area of a Trapezium found at: http://app.mymaths.co.uk/271-resource/area-of-a-trapezium http://app.mymaths.co.uk/271-homework/area-of-a-trapezium Save and complete the worksheet called AreaQ-S1.xlsx Now move on to the PAV2c powerpoint