Question

One side of a staircase is to be closed in by rectan-
gular planks from the floor to each step. The width
of each plank is 9 inches and their height are suc-
cessively 6 inches, 12 inches, 18 inches and so on.
There are 24 planks required in total. Find the area
in square feet
(a) 112.5
(b) 107
(c) 118.5
(d) 105

Explain the answer please​

Answer 1

Answer:

a) 112.5 square feet

Step-by-step explanation:

total no. of planks = 24

width of each plank = 9 inches

height of 1st plank = 6 inches

                 2nd        = 12 inches

                 3rd         = 18 inches and so on

let's start by calculating the area of 1st plank

area of rectangle = height x width = 6 x 9 = 54 sq inches

2nd plank = 12 x 9 = 108 sq inches

3rd plank = 18 x 9 = 162 sq inches

the trend shows that multiplying 54 by successive number of plank will give area of that particular plank or just adding 54 to the previously calculated area as

2 x 54 = 108 and 3 x 54 = 162 and so on.

54 + 4 = 108 and 108 + 54 = 162 an so on.

upon calculating and adding areas of 24 planks we get the total area as 16,200 square inches.

1 square inch = 0.00694444 square foot so,

16200 x 0.00694444 = 112.5 square feet

Answer 2

$\huge \tt a) \: \: 112.5 \: \: {ft}^{2}$