Area of Triangles, Parallelograms & Circles

Once a child can find the area of a rectangle by counting unit squares, the curriculum builds the other plane figures on top of it — and CTET tests how that bridge is built. The area of a parallelogram is base × height, where height is the perpendicular distance between the two parallel sides, NOT the slanting side. The classic Class VII demonstration is to cut a right-triangle off one end of the parallelogram and slide it to the other end, turning the shape into a rectangle of the same base and height — which is why the formula matches the rectangle. The area of a triangle is ½ × base × height, because any triangle is exactly half of a parallelogram (or rectangle) on the same base and between the same parallels. The most common student error here is using the slant side instead of the perpendicular height, so a good teacher always points to the right-angle mark. The area of a circle is πr² and the circumference (the 'perimeter' of a circle) is 2πr; CTET frequently mixes these two up on purpose, so read whether the question asks for the boundary (circumference, 2πr) or the surface inside (area, πr²). Use π = 22/7 when the radius is a multiple of 7, which keeps the arithmetic clean.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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