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Answer :
Let's take a look at the problems one by one:
Calculate the area of the figure with squares on each side of the rectangle.
Given a rectangle with length 24 cm and width 18 cm. Four identical squares of side 6 cm are placed on each side.
First, calculate the area of the rectangle:
[tex]\text{Area of the rectangle} = \text{Length} \times \text{Width} = 24\, \text{cm} \times 18\, \text{cm} = 432\, \text{cm}^2[/tex]
Calculate the area of one square:
[tex]\text{Area of one square} = \text{Side} \times \text{Side} = 6\, \text{cm} \times 6\, \text{cm} = 36\, \text{cm}^2[/tex]
Since there are 4 squares, calculate their total area:
[tex]\text{Total area of squares} = 4 \times 36\, \text{cm}^2 = 144\, \text{cm}^2[/tex]
The total area of the figure is the sum of the area of the rectangle and the total area of the squares:
[tex]432\, \text{cm}^2 + 144\, \text{cm}^2 = 576\, \text{cm}^2[/tex]
Calculate the area of the figure that is made of squares of side 5 cm.
Without specific details on the number of squares or configuration, the area of one square is:
[tex]\text{Area of one square} = 5\, \text{cm} \times 5\, \text{cm} = 25\, \text{cm}^2[/tex]
If more details were provided about the configuration or number of squares, we could calculate the total area.
Calculate the area of a rectangle after a piece is cut off.
The original rectangle has dimensions 30 cm by 24 cm.
Calculate the original area:
[tex]\text{Original area} = 30\, \text{cm} \times 24\, \text{cm} = 720\, \text{cm}^2[/tex]
A piece 8 cm by 6 cm is cut off. Calculate the area of the piece:
[tex]\text{Area of the piece} = 8\, \text{cm} \times 6\, \text{cm} = 48\, \text{cm}^2[/tex]
The area of the rectangle after the piece is cut off:
[tex]720\, \text{cm}^2 - 48\, \text{cm}^2 = 672\, \text{cm}^2[/tex]
Calculate parts related to square ABCD and rectangles inside it.
- Without specific dimensions, but given: Square ABCD is divided into rectangles ABEF and CDEF, which is further divided into 4 equal squares.
- (a) and (b) require dimensions, but if each small square is equal, and if needed dimensions/details are given, apply area and side calculations.
Calculate side M of a rectangle given figures A and B have the same area.
If figures A and B are assumed to be square and a rectangle, given the side of the square is 10 m:
[tex]\text{Area of the square} = 10\, \text{m} \times 10\, \text{m} = 100\, \text{m}^2[/tex]
Rectangle has the same area:
[tex]\text{Area of rectangle} = \text{Length} \, (M) \times \text{Width} = 100\, \text{m}^2[/tex]
Without a fixed width, we can only express M in terms of width using [tex]M = \frac{100}{\text{Width}}[/tex]. If the width is known, M can be calculated.
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