Question

A room is constructed along with the verandah around it surrounding all the four sides of the room. Dimensions of the room are 5.5 m long and 4 m wide. Verandah is of width 2.25 m. Find the area of verandah constructed?

Answer 1

Hint: Draw a diagram illustrating the information given in the question. Then it will be easy to find the area of verandah. There are two methods of finding the area of verandah:
1. Divide the verandah into smaller rectangles, and then calculate the dimensions of those rectangles then find the area of those rectangles and lastly add them to get the area of the verandah.
2. After drawing the diagram you will see that the verandah is nothing but a difference of a bigger rectangle and a smaller rectangle.

Complete step-by-step answer:

Since the question is about geometrical figures we will first draw it.

Suppose ABCD is a room and the surrounding area is the verandah. We have AB = 5.5 m and BC = 4 m.
It is given that the width of the verandah is 2.25 m. That means
ID = JA = LB = CK = 2.25 m.
Area of the verandah can be computed as the sum of the area of rectangles EFIJ, DIKC, LKGH, JABL.
Now,
JI = JA + AD + DI = 2.25 + 4 + 2.25 = 8.5 m
FI = 2.25 m
JL = IK = AB = 5.5 m
LH = 2.25 m
LK = JI = 8.5 m
Area of rectangle EFIJ = JI x FI = 8.5 m x 2.25 m
                                       = 19.125 $m^2$
 Area of rectangle LKGH = Area of rectangle EFIJ
                                            = 19.125 $m^2$
 Area of rectangle DIKC = DI x IK = 2.25 m x 5.5 m
                                            = 12.375 $m^2$
 Area of rectangle JABL = Area of rectangle DIKC
                                            = 12.375 $m^2$
Now the area of verandah is the sum of all the above rectangles.
Area of the verandah = 19.125 + 19.125 + 12.375 + 12.375
                                       = 63 $m^2$
So the area of verandah is 63 $m^2$.

Note: There is an alternate method to solve this problem.
Area of verandah = Area of rectangle EFGH – area of rectangle ABCD
                                = EF x FG – AB x BC
                                = (4 + 2.25 + 2.25)x(5.5 + 2.25 + 2.25) – 4 x 5.5
                                = 8.5 x 10 – 4 x 5.5
                                = 85 – 22 = 63
So the area of verandah is 63 $m^2$.