Triangles, parallelograms, trapeziums and circles aren't made of whole squares. Cut each one up and move the pieces into a shape you already know.
🟦 Area & Perimeter →Draw the rectangle round it. How much of it does the triangle fill?
Triangles
Half of its rectangle
base × height ÷ 2
Parallelograms
Slide the end across to make a rectangle
base × height
Trapeziums
Two of them make a parallelogram
(a + b) × height ÷ 2
Circles
Slices make a rectangle
π × r × r
Shapes made of parts
Split it into shapes you know
add the parts
Height
Always measured straight up from the base, at a right angle. Not along a sloping side.
Multiply the base by the height and halve it. Draw the rectangle round the triangle and you can see why: the pieces outside the triangle exactly match the pieces inside, so the triangle is half the rectangle.
Cut the triangle off one end and slide it to the other end: the parallelogram becomes a rectangle with the same base and the same height. The sloping side is longer than the height, so using it gives too big an answer.
Area = π × r × r, with π about 3.14. Cut a circle into thin slices and lay them top to tail: they make a shape that is nearly a rectangle, half the circumference (π × r) long and r high.
Children find the area of triangles and parallelograms at about 10 or 11. The trapezium and the circle usually follow at about 11 to 13.