2TH §8.1 area of triangles

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§8.1 Area of triangles

We do exercise 1 together, step by step.

By this we will discover a Formula for Calculating

the area of any Triangle.

A Movie is included, that explains it in a similar way.

Finally you're going to make some exercises from this §.

Calculating an area by enclosing:

If you have to calculate the area of a TRIANGLE,

you can first calculate the area of a RECTANGLE 

in which the triangle lies.

In other words: the triangle is enclosed by the rectangle.

More about this in the coming slides!

Work out in your head

and key in 

your answer in the next slide.

1a area= ....

SOLUTION:

area KLMN = 9 x 5 = 

area KPN = 3 x 5 : 2 = 

area PLM = 6 x 5 :2 = 

 area KLP =                  -                  -  

= 

45cm​2​​

7.5cm​2​​

15cm​2​​

45cm​2​​

7.5cm​2​​

15cm​2​​

22.5cm​2​​

Think about this.

Try to EXPLAIN.

Solution:

Both triangles are half of rectangle 

KRPN, so they have the same size.

Think about this.

Solution:

Triangle RLP and triangle LMP

also have the same size.

Think this over!

Try to explain.

Solution:

Triangles KPN and LMP together are 

just as big as triangle KLP.

So:

area KLP = 1/2 x area KLMN

Think this over!

Solution:

area KLMN = KL x PR

area KLP = 1/2 x area KLMN, so

area KLP = KL x PR : 2

After this first task, a Movie follows.

Note: the teacher talks about 'inches'.   An inch  ≈ 2.5 cm !

After the Movie, the THEORY from the book follows.

Question: 

The area of which triangle you cannot calculate 

right away?

ANS

1. ABC
2. KLM
3. PQR

TASK:

How to calculate the area of triangle PQR ?

What do we have to do first?

TASK:

How to calculate the area of triangle PQR ?

What length do we have to calculate first?

ANS

side ...

1. PQ
2. QR
3. RS

First  RS has to be calculated.

Because RS is the HEIGHT for BASE PQ.

RS is perpendicular to PQ.

To calculate height RS we have to use .....

Pythagoras' theorem we have to use here! As follows:

Homework

Do §8.1 Exercises 3 until 7

Check your work with the Solutionsbook

Send in your work in GC