Question

worksheet 26
solve the following.

1. each side of a square table

top measures 23 cm. find
its area.

1. mr. joshi bought a square photo

frame of side 41 cm. find its area.

1. the given image is of

a rectangular card,
which has a border
and a printed portion
in the middle. find the
area of the card.

1. rohan has covered his

fish tank with a wooden
plank of length 5 m and
breadth 3 m. find the
area of the plank.

time: minutes
teacher’s signature: ...............
26

Explanation:

Step1: <Formula for area of square>

The area of a square is given by \(A = s^2\), where \(s\) is the side - length of the square.
For the square table - top with \(s = 23\) cm, \(A=(23)^2=23\times23\).

Step2: <Calculate the product>

\(23\times23=(20 + 3)\times(20+3)=20\times20+2\times20\times3 + 3\times3=400+120 + 9=529\) \(cm^2\).

For the square photo - frame with \(s = 41\) cm, \(A=(41)^2=41\times41\).

Step3: <Calculate the product>

\(41\times41=(40 + 1)\times(40 + 1)=40\times40+2\times40\times1+1\times1=1600 + 80+1=1681\) \(cm^2\).

For the rectangular card:
The length of the printed portion is \(l_p=8\) cm and the width of the printed portion is \(w_p = 6\) cm. The border is \(2\) cm on each side.
The length of the card \(l=l_p+2 + 2=8 + 4=12\) cm.
The width of the card \(w=w_p+2 + 2=6 + 4 = 10\) cm.
The area of a rectangle is \(A=l\times w\).
So, \(A = 12\times10=120\) \(cm^2\).

For the wooden plank (rectangle) with \(l = 5\) m and \(w = 3\) m.
Using the formula \(A=l\times w\), we have \(A=5\times3 = 15\) \(m^2\).

Answer:

1. \(529\) \(cm^2\)
2. \(1681\) \(cm^2\)
3. \(120\) \(cm^2\)
4. \(15\) \(m^2\)