Areas and volumes

Objectives:

• Area of rectangles and triangles

• Area of parallelograms and trapeziums

• Volume of cuboids

• Parts of a circle, circumference and area.

 

Area of a rectangle:

 

Area of a triangle:

More: Area of a triangle inside a rectangle

Area of a parallelogram:

Area of a trapezium:

(Note: this shape is also known as a trapezoid, but for your exam just use trapezium!)

Cuboids

A cuboid is a box-shaped object. Click the image below for more information.

V = l × w × h

Nets

A 'net' is the shape you get when you cut along the edges of a three dimensional object and lay it out flat.

 

Parts of a circle:

Copy the picture below, label the green and blue sections:

Answer is here.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Circle: Area and circumference

Homework:

P162  Ex 18.1     Q 3

P165  Ex 18.2A  Q3

P165  Ex 18.2B  Q 1b, Q2b

P170  Ex 18.3B  Q 1, 2

P172  Ex 18.4     Q 3

P174  Ex 18.5A   Q 1 - 9

P176  Ex 18.5B  Q 1c, 1d, 2c, 2d.

P177  Ex 18.5C  d, e

Similar Triangles and Sine, Cosine, Tangent.

• Identify similar shapes

• Use Sin, Cos and Tan for acute angles

Similarity

Two shapes are Similar if the only difference is size (and possibly the need to turn or flip one around). Information on similar triangles.

See if you can figure out how tall a tree is without having to measure its height:

Right angled triangle ratios

Sine, Cosine and Tangent ratios

Remember:

Sohcahtoa

Soh...	Sine = Opposite / Hypotenuse
...cah...	Cosine = Adjacent / Hypotenuse
...toa	Tangent = Opposite / Adjacent

Click the image below for some extra exercises and further information:

Homework:

P289 Ex1 Q. 6, 11, 13, 16, 17

P293 Ex 2 Q. 17-20

P293 Ex 3 Q. 4, 6, 7, 10, 11, 12

Angle Properties

• Identify: Supplementary, vertically opposite, corresponding and alternate angles.

• Know that angles of a triangle add up to 180°

• Know that the exterior angle of triangle is equal to the sum of the two interior opposite angles.

• Know that angles of a quadrilateral add up to 360°

Supplementary Angles (add to 180°)

 

Vertically Opposite Angles..... are equal

 

Corresponding Angles (look for an 'F' shape)...... are equal

 

Alternate Angles (look for a 'Z' shape)....are equal

Angles of a triangle add up to 180°

A + B + C = 180°

Exterior angle of triangle is equal to the sum of the two interior opposite angles.

C = A + B

Angles of a quadrilateral add up to 360°

80° + 100° + 90° + 90° = 360°

Homework:

P153  Ex 16.4C  Q3-6 

P156  Ex 17.1B  Q4-8

P158  Ex 17.2     Q3, 5, 6

P160  Ex 17.3A  Q3, 4

P160  Ex 17.3B   Q1, 4