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Class 8 Maths: Area, 8 practice questions with answers

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These are 8 practice questions on Chapter 7, Area, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover tiles for a floor, an L-shaped room, a triangle whose base doubles while its height halves, one fence that shares a field equally, a five-sided wall split into simpler pieces, a parallelogram's height from its slanting side, a rhombus from its side and one diagonal, and two trapezium beds whose parallel sides add up to the same length. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-worked by a test script and each question was compared with the chapter's examples, activities and exercises, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 2, Chapter 7, printed pages 148 to 171):

Rectangles and borders

Question 1. A floor 3 m long and 2 m wide is to be covered with square tiles of side 25 cm, with no gaps and no cutting. How many tiles are needed?

Answer: 96 tiles. 3 m = 300 cm and 2 m = 200 cm. Along the length, 300 ÷ 25 = 12 tiles fit in a row, and along the width 200 ÷ 25 = 8 rows, so the floor takes 12 × 8 = 96 tiles. (Unit squares filling a rectangle, length × width, page 149.)

Question 2. An L-shaped room is a rectangle 8 m by 6 m with a 3 m by 2 m rectangle missing from one corner. Find its area in two different ways.

Answer: 42 square m. Way 1: the full rectangle is 8 × 6 = 48 square m; take away the missing corner, 3 × 2 = 6 square m: 48 − 6 = 42 square m. Way 2: cut the L into two rectangles. If the 3 m by 2 m gap is along the 8 m side, one piece is the full 8 m by 4 m strip (32 square m) and the other is the 5 m by 2 m piece beside the gap (10 square m): 32 + 10 = 42 square m. Both ways agree. (Areas built from rectangles, page 149.)

Triangles

Question 3. A triangular plot has a side of 12 m, and the height to that side is 7 m. Its area is 42 square m. A second plot has a base twice as long, 24 m, and a height half as long, 3.5 m. How does its area compare with the first plot's, and why?

Answer: the same, 42 square m. Area = 1/2 × 24 × 3.5 = 42 square m, the same. Doubling the base doubles the area and halving the height halves it, so together they leave it unchanged. (The area of a triangle, pages 153 to 155.)

Question 4. Two brothers are to share a triangular field of area 54 square m equally, using one straight fence that starts at one corner. Where must the other end of the fence be, and why are the two pieces then equal?

Answer: at the midpoint of the side facing that corner; each piece is then 27 square m. The fence splits the field into two triangles with the same height, measured from the corner to the facing side. Their bases are the two parts of that side. Equal bases with the same height give equal areas, so the fence must end at the midpoint of the facing side, and each brother gets 54 ÷ 2 = 27 square m. (A line from a corner to the midpoint of the opposite side, page 155.)

Polygons and quadrilaterals

Question 5. The front wall of a small house is a rectangle 10 m wide and 6 m tall, with a triangular part on top whose base is the 10 m top edge and whose height is 4 m. What is the area of the whole five-sided wall?

Answer: 80 square m. Cut the pentagon into the pieces whose areas are known: the rectangle is 10 × 6 = 60 square m and the triangle is 1/2 × 10 × 4 = 20 square m, so the wall is 60 + 20 = 80 square m. Any polygon can be cut into triangles (the rectangle itself is two triangles of 30 square m), so this always works. (The area of any polygon, page 159.)

Question 6. A parallelogram has a base of 15 cm and a slanting side of 10 cm whose top end is 6 cm to the right of its bottom end. Find its height and its area.

Answer: height 8 cm, area 120 square cm. The slanting side, the height and the 6 cm shift make a right triangle with the 10 cm side as its longest side, so the height is the square root of 100 − 36 = 64, that is 8 cm. The area is base × height = 15 × 8 = 120 square cm. (The area of a parallelogram, base × height, pages 161 to 163; the right-triangle step uses the Baudhayana-Pythagoras theorem from Chapter 2 of this book.)

Question 7. A rhombus has sides of 10 cm, and one of its diagonals is 12 cm. Find the other diagonal, and hence the area of the rhombus.

Answer: 16 cm, and an area of 96 square cm. The diagonals of a rhombus cut each other in half at right angles. So half of the 12 cm diagonal (6 cm), half of the other diagonal and a 10 cm side make a right triangle with the side as its longest side. By the Baudhayana theorem, the half-diagonal is the square root of 100 − 36 = 64, that is 8 cm, so the other diagonal is 16 cm. Then the area = 1/2 × 12 × 16 = 96 square cm. Check: the 4 small triangles each have area 1/2 × 6 × 8 = 24, and 4 × 24 = 96. (The area of a rhombus from its diagonals, pages 164 and 165; the right-triangle step uses the Baudhayana-Pythagoras theorem from Chapter 2 of this book.)

Question 8. Two garden beds are trapeziums, both with their parallel sides 4 m apart. Bed A's parallel sides are 9 m and 5 m; bed B's are 8 m and 6 m. Without drawing them, which bed has the larger area? What do all trapeziums with height 4 m and parallel sides adding up to 14 m have in common?

Answer: they have the same area, 28 square m; every such trapezium has area 28 square m. A trapezium's area is half the height times the sum of the parallel sides. For bed A that is 1/2 × 4 × (9 + 5) = 28, and for bed B 1/2 × 4 × (8 + 6) = 28: equal. Since only the sum of the parallel sides (with the height) matters, every trapezium with height 4 m and parallel sides adding up to 14 m has area 28 square m, however the 14 m is split. (The area of a trapezium, pages 166 to 168.)

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Sources

All opened and read on 31 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 147.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Area, Class 8 worksheet. Printable, in English, Hindi and Marathi, with an answer key.