Page 209 - Math Genius C5

E:\Working\Orange_Education\Math_Genius_5\Open_Files\CHAP_11
\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

Example 5: Find the area of a square whose length is 14 cm. 14 cm Example 2: Find the area of the following figure.
Solution: Length of a side of the square = 14 cm 8 cm

Area of the square = side × side 14 cm 6 cm
= 14 cm × 14 cm = 196 sq. cm 10 cm 12 cm 8 cm
Example 6: Find the area of a square whose perimeter is 84 cm.
Solution: Perimeter of the square = 84 cm 24 cm

Side of the square = Perimeter of the square ÷ number of sides Solution: We divide the given figure into rectangles and a square.
= (84 ÷ 4) cm = 21 cm Area of rectangle A = 10 cm × 4 cm = 40 sq. cm

Now, area of the square = side × side Area of rectangle B = 12 cm × 4 cm 4 cm
= (21 × 21) sq. cm = 441 sq. cm = 48 sq. cm 6 cm 8 cm
Thus, the area of the square is 441 sq. cm. Area of square C = 8 cm × 8 cm 10 cm A 12 cm 8 cm
= 64 sq. cm 4 cm B C

Think Tank Critical Thinking Thus, the area of the given shape 24 cm
What will be the length of the side of a square whose area and perimeter are equal? = Area of square C + Area of rectangle B + Area of rectangle A

= (64 + 48 + 40) sq. cm = 152 sq. cm.
FACTS
Two rectangles can have the same perimeter but very different areas. A long, skinny rectangle AreA of A triAngle
such as 1 cm by 9 cm has a perimeter of 20 cm and an area of 9 sq. cm. On the other hand, a square- Look at the square shown alongside.
like rectangle such as 5 cm by 5 cm also has a perimeter of 20 cm, but its area is much larger, i.e.,
25 sq. cm. Area of the square = 6 cm × 6 cm = 36 sq. cm
A diagonal divides a square into two halves. Each half is a triangle.
AreA of A CompoSite figUre Thus, the area of a triangle is half the area of the square. 6 cm

Example 1: Find the area of the following figure. Area of each triangle = Area of the square

5 cm 2 6 cm
36
= sq. cm = 18 sq. cm.
2
1 cm
3 cm
1 cm Is this also true for a rectangle? Let us see.
Here, a rectangle whose length is 8 cm and breadth is 6 cm is 6 cm
given.

5 cm Area of the rectangle = 8 cm × 6 cm = 48 sq. cm 8 cm
Solution: The given figure can be divided into three rectangles as (I) 1 cm
shown. Again, the diagonal divides the rectangle into two equal halves, and each half is a triangle.

Area of rectangle (I) = 5 cm × 1 cm = 5 sq. cm 1 cm 3 cm So, area of each triangle = 48 ÷ 2 sq. cm = 24 sq. cm.

Area of rectangle (II) = 3 cm × 1 cm = 3 sq. cm (II) Now, let us find the area of the triangles shown below.
Area of rectangle (III) = 5 cm × 1 cm = 5 sq. cm ( a) ( b)
(III)
Area of the complete figure

= area of rectangle (I) + area of rectangle (II) + area of rectangle (III)
= 5 sq. cm + 3 sq. cm + 5 sq. cm = 13 sq. cm

Mathematics-5 207207
Mathematics-5