Step by step
The question
Question: find the area of a triangle with base 12 cm and height 7 cm.
1 Half of a rectangle
The height goes straight up from the base to the top corner.
It makes a right angle with the base.
Draw a box around the triangle: a rectangle 12 cm long and 7 cm high.
The height cuts the box into two smaller boxes.
The slanted left side cuts the left box from corner to corner.
Half is inside the triangle, half is outside.
The slanted right side cuts the right box the same way.
Half of each small box is inside.
So the triangle fills exactly half of the whole box.
2 Use the rule
The box is base times height.
The triangle is half of it: A = ½ × b × h.
Now put the numbers in: b = 12 and h = 7.
12 times 7 is 84.
That is the whole rectangle.
Half of 84 means 84 divided by 2.
That is 42.
So the area is 42 cm².
Let's look back.
First: half of a rectangle.
Last: use the rule.