Area
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Area of Rectangles and Why Perimeter Is Not Area
Part of: Area of plane shapes
The area of a rectangle is length times width, found by counting unit squares. Perimeter is the length of the boundary, which is a different thing. Two rectangles can have the same perimeter but different areas, and a shape with a larger perimeter can have a smaller area. For a path around a park, subtract the area of the park from the area of the bigger rectangle that includes the path.
Why it matters. Confusing area and perimeter is a very common mistake. Knowing the difference helps in tiling floors, fencing fields and many real tasks.
Try it in two minutes
- Draw a 6 by 2 rectangle and a 5 by 3 rectangle on squared paper. Count the squares and measure the boundary of each.
- Ask your child which has the larger area and which has the longer boundary.
- Ask them to design two rectangles with the same area and different perimeters.
Try at home. Use string of fixed length to make different rectangles on squared paper and compare their areas.
Area of a Triangle
Part of: Area of plane shapes
A triangle drawn inside a rectangle with the same base and height covers exactly half of it. So the area of a triangle is half of base times height, where the height is the perpendicular distance from the opposite corner to the base. Any side can be the base if you use the matching height. A line from a corner to the midpoint of the opposite side cuts a triangle into two parts of equal area.
Why it matters. Triangles are the building blocks of other shapes, so this idea is used for all polygons. It also gives children practice with working backwards to a height or a base.
Try it in two minutes
- Draw a rectangle 8 cm by 5 cm and a diagonal. Ask your child for the area of each half.
- Draw a triangle with base 8 cm and height 5 cm and compare its area with the rectangle's.
- Ask your child to find the area using a different side as base.
Try at home. Cut a rectangle of paper along a diagonal and show the two halves match.
Area of a Parallelogram
Part of: Area of plane shapes
A parallelogram can be cut along a perpendicular from one corner and the cut triangle moved to the other end to make a rectangle of equal area. So the area of a parallelogram is base times height, where the height is the perpendicular distance between the two parallel sides, not the slanted side. Either pair of sides can be the base if you use the matching height.
Why it matters. Children often multiply the two side lengths. Seeing the rectangle hidden inside a parallelogram corrects this and prepares them for rhombuses and trapeziums.
Try it in two minutes
- Draw a parallelogram on paper with a slanted side. Draw the perpendicular height.
- Cut off the triangle at one end and slide it to the other end to make a rectangle.
- Ask your child to find the area using the base and the height.
Try at home. Ask your child to compare a leaning parallelogram and a rectangle with the same base and height.
Area of a Rhombus
Part of: Area of plane shapes
A rhombus is a parallelogram with all sides equal, so base times height works. Its diagonals cut each other at right angles and in half. This gives another formula: area is half the product of the two diagonals. A rhombus with diagonals 16 and 12 has area 1/2 × 16 × 12 = 96. If the side and one diagonal are known, the Baudhāyana theorem gives the other diagonal.
Why it matters. Having two formulas gives children a way to check their answers and choose the one that suits the information given.
Try it in two minutes
- Draw a rhombus with two diagonals of 8 cm and 6 cm. Ask your child to find its area.
- Ask them to find the area as four small triangles and check.
- Ask them what happens to the area if one diagonal is doubled.
Try at home. Fold a paper kite shape and ask your child to explain why the area is half the product of the diagonals.
Area of a Trapezium and Other Polygons
Part of: Area of plane shapes
A trapezium has one pair of parallel sides. If they are a and b long and the distance between them is h, the area is 1/2 × h × (a + b). Two copies of the trapezium joined together make a parallelogram with base a + b and height h, so one trapezium has half its area. Any polygon can be split into triangles, so its area is the sum of their areas.
Why it matters. Fields, roofs and cross-sections are often trapezium-shaped. Splitting shapes into simpler pieces is a useful problem-solving skill.
Try it in two minutes
- Draw a trapezium with parallel sides 6 cm and 10 cm and height 4 cm and find its area.
- Make two copies on paper and join them into a parallelogram. Ask how the areas compare.
- Draw a four-sided shape and ask your child to split it into two triangles.
Try at home. Cut out two identical paper trapeziums and fit them together to see the parallelogram.
What your child will practise
- Area of a Parallelogram: Jungle Quick Fire (Quick Fire)
- Area of a Rhombus: Ocean Puzzle (Clue Puzzle)
- Area of a Trapezium and Other Polygons: Desert Quick Fire (Quick Fire)
- Area of a Triangle: Number Quest (Collect the Answer)
- Area of Rectangles and Why Perimeter Is Not Area: Lab Explorer Quest (Collect the Answer)
- Quiz: Area of Rectangles and Why Perimeter Is Not Area (8 questions)
- Quiz: Area of a Parallelogram (8 questions)
- Quiz: Area of a Rhombus (8 questions)
- Quiz: Area of a Trapezium and Other Polygons (8 questions)