Properties of Triangles Are in Fact a Major Area of Study in Year 9

Terrific Triangles

Some people would argue that triangles are the most important shape there is. This is because of their amazing ability to support weight within structures, such as in the roof of a building.

Properties of triangles are in fact a major area of study in year 9.

What we are concerned with is finding the area of triangles.

Previously it was stated that;

All formulas for the areas of shapes come back to the idea of the area of a rectangle.

With that in mind look at the triangles below;

Question 1)

Write the definition of each of the following types of triangles and label the triangles above as either;

a)Scalene -

b)isosceles -

c)right angled -

d)equilateral -

Question 2)

On the pictures above draw how each triangle can be related to a rectangle.

Question 3)

If each square on the grid is 1cm2 estimate to the best of your ability the area of each triangle and each rectangle you made in question 2.

Triangle 1 area –

Rectangle 1 area -

Triangle 2 area –

Rectangle 2 area –

Triangle 3 area –

Rectangle 3 area –

Question 4)

What do you notice about the area of each triangle compared to the corresponding rectangle?

Question 5)

What is the formula for finding the area of a rectangle?

Question 6)

What do you need to do to the formula for the area of a rectangle to find the area of a triangle?

There is one difference in the terminology we use for the formula for area of triangles. Instead of using length and width we use base and height.

Question 7)

Write the formula for the area of a triangle using words

Question 8)

Write the formula for the area of a triangle using letters

Congratulations! You have just made your first Mathematical theory!

But we’re not quite done yet. You have a theory and it seems to have worked but it’s only been tested on 3 examples. It’s really just not enough times to make sure our theory is working and that we understand how it works and how to apply it effectively.

Question 9)

On the triangles below mark the base length and height. (Be very careful where you mark the height, you may want to look back at previous questions)

Question 10)

Accurately measure the dimensions of the triangles from Question 9 and calculate the areas of each.

Question 11)

a) What do you notice about the 2 scalene triangles from question 9?

b) Where did you mark the base?

c) Draw a rectangle around the second last triangle. Is it half of a rectangle?

D) What do you need to make sure of when you label the base of a triangle?

Question 12)

Accurately draw 10 different triangles making sure they are a mix of the four types defined in question 1. Calculate the areas of each triangle showing full working out.

Question 13*)

If the area of a triangle is 24cm2 and the base is twice the length of the height, find the length and height of the triangle.

Question 14*)

The hexagon below can be split into 6 identical isosceles triangles. Calculate the area of the hexagon.