NCERT Solutions for Class 5th Maths Chapter 7 Drawing on a grid, and building with 3 and 4 pieces — Shapes from the Rhombus
Book page 99 Updated on2026-09-19
Q1.
In the grid given below, draw two different kites and parallelograms each.The grid given in the book, page 99.
Answer
Use the corners of the grid squares as your points. Here are two kites and two parallelograms you can copy.
How to draw a kite on the grid
Draw a straight line down the grid. This is the mirror line.
Mark a point on the line near the top and another near the bottom.
Mark two more points, one to the left and one to the right of the line, both the same number of squares away and on the same grid row.
Join the four points in order. The two upper sides are equal and the two lower sides are equal — that is a kite.
How to draw a parallelogram on the grid
Draw the bottom side — say 5 squares long.
Step across and up from one end, for example 2 squares right and 3 squares up. Mark the point.
Make exactly the same step from the other end of the bottom side. Mark that point too.
Join the four points. The top and bottom are equal, the two slanting sides are equal — that is a parallelogram.
Two kites (blue and green) and two parallelograms (yellow and pink), all drawn on grid corners.
Why the grid makes it easy: Counting squares is a way of measuring without a ruler. If you count the same number of squares on both sides of the mirror line, the two sides must be equal.
Did you notice? Kite 2 has all four sides equal. A kite with all four sides equal is a rhombus. So a rhombus is a special kind of kite.
Q2.
Now, use 3 triangles from the rhombus to form shapes. How many sides do each one of them have? Using 3 triangular pieces of the rhombus, try creating a (a) 3-sided shape, (b) 4-sided shape, and (c) 5-sided shape.The rhombus and its four triangular pieces.
Answer
(b) and (c) work easily. (a) does not — three of these pieces will not close up into a triangle. Here is what happens when you actually try.
Two pieces make a rectangle; where the third piece is stuck on decides how many sides the whole shape has.
(b) A 4-sided shape
Put two pieces together along their slanting sides to make a rectangle.
Take the third piece and place its long side exactly along the top of the rectangle.
The outline now has 4 corners — it is a four-sided shape (a trapezium).
(c) A 5-sided shape
Make the same rectangle from two pieces.
Place the third piece on the top edge, but this time put its short side along the top, starting from the left corner.
Because the short side is shorter than the top of the rectangle, a step (a notch) is left. That step adds an extra corner, so the outline has 5 sides.
(a) A 3-sided shape
Two pieces alone already make a triangle — that is half the rhombus.
Now try to add a third piece anywhere along its edges.
Every time, one more corner appears, so you end up with 4 or 5 sides, never 3.
The reason: for the outline to stay a triangle the new piece must have a side exactly as long as the edge it is covering, and none of its sides is the right length.
Worth knowing: If your rhombus were made of two equilateral triangles (a wider, flatter rhombus), then three pieces would close up into a triangle. Ask your teacher for such a rhombus and try it — the answer to a shape question can depend on the exact shape you start with.
Q3.
Which of these shapes can be made with all 4 pieces? Try and find out. (a) Square (b) Rectangle (c) Triangle (d) Pentagon (5-sided) (e) Hexagon (6-sided) (f) Octagon (8-sided)The rhombus and its four triangular pieces.
Answer
(b) Rectangle, (c) Triangle, (d) Pentagon and (e) Hexagon can be made. (a) Square and (f) Octagon cannot.
Shape
Can you make it?
Reason
(a) Square
No
Two pieces make a rectangle whose sides are the two different half-lines of the rhombus. Putting two such rectangles side by side still gives a rectangle, never a square.
(b) Rectangle
Yes
Two pieces make one rectangle; place a second such rectangle beside it, long side to long side.
(c) Triangle
Yes
Four pieces make one big triangle with every side exactly twice as long as the piece's sides.
(d) Pentagon
Yes
Build the rectangle from three pieces and stick the fourth on so that it leaves one step.
(e) Hexagon
Yes
Stick the pieces on so that two steps are left in the outline.
(f) Octagon
No
Four triangles have 4 × 3 = 12 edges in all. Joining them uses up at least 3 pairs, that is 6 edges. So at most 6 edges are left on the outside — six sides is the most you can get.
For the triangle, join the middle points of the sides of a big triangle — it falls apart into 4 equal small triangles.
Why the big triangle always works: Mark the middle point of each side of any triangle and join those three points. The triangle splits into 4 equal triangles, each exactly half the size of the original in every length. So four of our pieces can always be put back together into a triangle twice as long on every side.
Did you know? If a rhombus happened to have one line exactly twice as long as the other, then its four pieces would make a square. Measure your rhombus and see how far it is from that.