An Introduction to 2-D Shape

Slideshow 15, MathematicsMr Richard Sasaki, Room 307

Objectives• Recall names of certain elements of

basic shapes• Recall formulae to find attributes to

certain basic shapes• Apply these formulae to finding

missing values for shapes

Square RootingWe need to have a brief look at how to square root. For shapes we only need to consider the positive root.

What is ? 3How did we get ?

We considered the number we multiply by itself to get . Square rooting is the opposite of squaring.

√16=¿4 √81=¿9√1=¿1 √0.25=¿0.5

Two Dimensional ShapesShapes that are flat are called 2D Shapes. We will learn about these in detail in Chapter 5. For now, we will use basic properties.

Let’s review some shape names.

Square Rectangle (Oblong)

Triangle

CircleParallelogram

QuadrilateralsQuadrilaterals are shapes with edges.4The examples we saw just now were the , the and the . square rectangle parallelogramThe Square

All lengths are equal and edges meet at 90o.

𝐴𝑟𝑒𝑎=¿𝐴=¿

( h𝑙𝑒𝑛𝑔𝑡 )2

𝑙=¿√ 𝐴𝑙2

QuadrilateralsThe Rectangle

A rectangle has parallel sides that are equal in length and edges meet at 90o.

𝐴𝑟𝑒𝑎=¿ h𝑙𝑒𝑛𝑔𝑡 × h𝑤𝑖𝑑𝑡𝑤

𝑙

𝐴=¿𝑙𝑤𝑙=¿𝐴𝑤

𝑤=¿𝐴𝑙

QuadrilateralsThe Parallelogram

𝑏

h

A parallelogram has two pairs of parallel sides and two pairs of equal angles.

𝐴𝑟𝑒𝑎=¿𝐴=¿

𝑏𝑎𝑠𝑒×h h𝑒𝑖𝑔 𝑡

𝑏=¿𝐴hh=¿𝐴𝑏

h𝑏There are of course other quadrilaterals. We will learn about them in Chapter 5.

Other ShapesThe Triangle Triangles have three

edges and three angles.

𝐴𝑟𝑒𝑎=¿12×𝑏𝑎𝑠𝑒×h h𝑒𝑖𝑔 𝑡

𝑏

h

𝐴=¿12 h𝑏 𝑏=¿2𝐴h h=¿2𝐴𝑏The Circle Circles have 1 curved edge

(or infinite edges).

𝑟

𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒=¿𝐶=¿2𝑟

2×𝜋×𝑟𝑎𝑑𝑖𝑢𝑠𝑟=¿

𝐶2

𝐴𝑟𝑒𝑎=¿𝜋× (𝑟𝑎𝑑𝑖𝑢𝑠 )2

𝐴=¿𝜋𝑟 2 𝑟=¿√ 𝐴

SubstitutionThere are of course many other shapes to look at in Chapter 5.Let’s try an example.

ExampleAn isosceles triangle has base 4cm and height 10cm. Calculate the area.

4𝑐𝑚

10𝑐𝑚

Let’s label the values given on the triangle.

𝐴=¿12h𝑏¿12×4×10¿20𝑐𝑚2

Note: Area is measured in square units.

Answers – Very Easy / Easy

𝐴=16 𝑐𝑚2

𝐴=6𝑚2

𝐴=24𝑐𝑚2

𝐴=40𝑐𝑚2

𝐴=35𝑐𝑚2

𝐴=25𝑐𝑚2

𝐴=144 𝑐𝑚2

𝐴=2𝑚2

𝑙=4𝑐𝑚No, we need its base and height or an angle.

𝐴=16𝜋 𝑐𝑚2

𝐶=8𝜋𝑐𝑚𝑙=6𝑐𝑚

The square

Answers – Medium / Hard 32𝑐𝑚2

8𝑐𝑚4𝑐𝑚

9𝑐𝑚2

𝑟𝑎𝑑𝑖𝑢𝑠𝐴=32𝑘𝑚2 ,𝑏=4𝑘𝑚16𝑘𝑚The parallelogram

1,400,000𝑚2

28𝑐𝑚2

12𝑐𝑚

51𝑐𝑚2

3𝑐𝑚12𝑐𝑚𝐴𝑐𝑖𝑟𝑐𝑙𝑒

42.25𝜋𝑐𝑚2𝑜𝑟 6.52 𝜋𝑐𝑚2

9𝑐𝑚