Question

(1) A side of a square handkerchief is 15.2 cm. What is its area?

(2) The area of a rectangle is 148.75 sq m. If its breadth is 8.5 m, what is its length?

(3) The length of a rectangular mat is 4 m and its breadth is 2.5 m. A 0.1 m wide border is attached to it on all four sides. What is the area of the border?

Answer 1

(1) Side of the square handkerchief = 15.2 cm
Area of the square handkerchief = Side × Side
= 15.2 × 15.2 cm²
= 231.04 cm²

(2) Let length of the rectangle be l m.
Breadth of the rectangle = 8.5 m
Area of the rectangle = 148.75 m²
$\Rightarrow$length × breadth = 148.75
$\Rightarrow$l × 8.5 = 148.75
$\Rightarrow l=\frac{148.75}{8.5}$
$\Rightarrow$l = 17.5
∴ Length of the rectangle is 17.5 m.

(3)

Let PQRS be the rectangular mat that has a border measuring 0.1 m along it. From the given information, we get the figure ABCD that is also a rectangle.
Length of PQRS = 4 m
Breadth of PQRS = 2.5 m
Area of PQRS = length × breadth
= 4 × 2.5 m²
= 10 m²
Now, there is a border measuring 0.1 m.
∴ Length of ABCD = 4 + 0.1 + 0.1 = 4.2 m
Breadth of ABCD = 2.5 + 0.1 + 0.1 = 2.7 m
Area of ABCD = length × breadth
= 4.2 × 2.7 m²
= 11.34 m²
Area of the border = Area of ABCD − Area of PQRS
= 11.34 m² − 10 m²
= 1.34 m²