Look at this rectangle on the board. It is 6 squares wide and 4 squares tall, with one straight line drawn from corner to corner.

That line splits the rectangle into two triangles. What fraction of the whole rectangle is each triangle?

On the board, perpendicular height means how far the top point stands straight up above the base, measured at a right angle, never along the slanting side. We will look at four triangles, each with area ½ × base × height. For the first ones, watch how each sits as half of a box with the same base and height, then see what happens to the height on the last one.

Today we work through three triangles together on the board. First a right triangle with base 5 and height 4. Then a taller one with base 5 and height 8. Last a wide flat one with base 12 and height 3.

Before each answer appears, say what half of base times height comes to. For each one we also draw the rectangle it fits inside, so we can see the triangle is exactly half.

Today we work out four triangle areas, then a trickier one where we know the area and find the missing height.

• base 4 cm, height 6 cm
• base 10 cm, height 5 cm
• base 7 cm, height 4 cm
• base 6 cm, height 6 cm

The stretch: a triangle has area 18 cm² and base 9 cm, how tall is it?