Download presentation
Presentation is loading. Please wait.
1
Awkward Triangle
2
What’s the exact area of this triangle?
Awkward Triangle (not to scale) 3 15 3 What’s the exact area of this triangle? Answer = 1 (based on 1/8 of the octagon in “From all Corners” scaled up by a factor of 12 ).
3
Use the Cosine Rule to determine angle 𝐴:
Awkward Triangle (not to scale) 3 15 3 One approach: Use the Cosine Rule to determine angle 𝐴: 𝑎 2 = 𝑏 2 + 𝑐 2 −2𝑏𝑐 cos 𝐴 Then use the formula for the area of a triangle: 𝐴𝑟𝑒𝑎= 1 2 𝑏𝑐 sin 𝐴 𝐴
4
Awkward Triangle 2 6 3 2 = 3 2 + 15 3 2 −2 3 15 3 cos 𝐴
15 3 𝐴 = − cos 𝐴 8 3 = −2 5 cos 𝐴 cos 𝐴 = sin 𝐴 = 2 5 Area is given by: 𝐴𝑟𝑒𝑎= =𝟏 𝐴 1 5 2
6
Awkward Triangle (not to scale) 3 15 3 Another option would be to use Heron’s formula. For triangle with sides 𝑎,𝑏,𝑐 Area = 𝑠 𝑠−𝑎 𝑠−𝑏 𝑠−𝑐 where 𝑠= 1 2 𝑎+𝑏+𝑐 Answer = 1 (based on 1/8 of the octagon in “From all Corners” scaled up by a factor of 12 ).
7
Awkward Triangle Using Heron’s formula with:
𝑎= 3 𝑏= 𝑐= 𝑠= Area = − − − = − = − = =𝟏 Answer = 1 (based on 1/8 of the octagon in “From all Corners” scaled up by a factor of 12 ).
8
𝟏 Awkward Triangle What’s the exact area of this triangle? 2 6 3 3
(not to scale) 3 15 3 What’s the exact area of this triangle? 𝟏 Answer = 1 (based on 1/8 of the octagon in “From all Corners” scaled up by a factor of 12 ).
9
RESOURCES
10
What’s the exact area of this triangle?
Awkward Triangle (not to scale) 3 15 3 What’s the exact area of this triangle? SIC_38
11
Awkward Triangle Awkward Triangle
B Awkward Triangle What’s the exact area of this triangle? 𝟓 𝟏 𝟐 𝟐 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟓 𝟐 𝟐 𝟐 𝟐 𝟒 (not to scale) SIC_38 SIC_38
12
Awkward Triangle Awkward Triangle
C D Awkward Triangle What’s the exact area of this triangle? 𝟕𝟖 𝟑 𝟔 𝟑 𝟐 𝟑 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟑𝟎 𝟑 𝟐 𝟑 𝟑 𝟔 (not to scale) SIC_38 SIC_38
13
Awkward Triangle Awkward Triangle
F Awkward Triangle What’s the exact area of this triangle? 𝟔𝟓 𝟓 𝟐 𝟏𝟎 𝟓 𝟓 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟕𝟎 𝟏𝟎 𝟏𝟎 𝟐 𝟒 𝟓 𝟓 (not to scale) SIC_38 SIC_38
14
Awkward Triangle Awkward Triangle
H Awkward Triangle What’s the exact area of this triangle? 𝟖𝟗 𝟐 𝟏 𝟐 𝟓 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟎 𝟐 𝟐 𝟓 𝟐 𝟐 (not to scale) SIC_38 SIC_38
15
Awkward Triangle Awkward Triangle
J Awkward Triangle What’s the exact area of this triangle? 𝟏𝟐𝟐 𝟒 𝟏𝟎 𝟒 𝟏𝟎 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟕 𝟐 𝟏 𝟓 𝟐 (not to scale) SIC_38 SIC_38
16
Awkward Triangle Awkward Triangle
What’s the exact area of this triangle? 𝟏𝟑 𝟐 𝟓 𝟐 𝟓 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟐𝟒 𝟑 𝟔 𝟐 𝟓 𝟔 𝟔 (not to scale) SIC_38 SIC_38
17
Awkward Triangle Awkward Triangle
M N Awkward Triangle What’s the exact area of this triangle? 𝟏𝟖𝟏 𝟑 𝟐 𝟑 𝟓 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟐 𝟔 𝟑 𝟓 𝟔 𝟑 (not to scale) SIC_38 SIC_38
18
Awkward Triangle Awkward Triangle
O P Awkward Triangle What’s the exact area of this triangle? 𝟏𝟕 𝟑 𝟓 𝟐 𝟓 𝟑 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟑 𝟑 𝟐 𝟓 𝟑 (not to scale) SIC_38 SIC_38
19
Awkward Triangle Awkward Triangle
X Awkward Triangle What’s the exact area of this triangle? 𝟔𝟓 𝟓 𝟐 𝟏𝟎 𝟓 𝟓 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟑 𝟐 𝟓 𝟐 𝟓 (not to scale) SIC_38 SIC_38
20
Awkward Triangle Awkward Triangle
Y Z Awkward Triangle What’s the exact area of this triangle? 𝟏𝟐𝟐 𝟒 𝟏𝟎 𝟒 𝟏𝟎 (not to scale) Awkward Triangle What’s the exact area of this triangle? 𝟏𝟕 𝟐 𝟏 𝟓 𝟐 (not to scale) SIC_38 SIC_38
21
Note to Teacher Tasks W, X, Y and Z have angle A >90⁰ and so cosine A is negative. This could throw pupils and so should really be given as an extension, given the way the worked solution goes. If calculators are allowed (to speed the task up, say) then there is no real problem. Tasks W, X, Y and Z are tasks E, K, I and J, respectively, with sides 𝑎 and 𝑐 swapped over.
22
REFERENCE MATERIAL
Similar presentations
