Question
Find the equation to find the total area of the given figure.
![](data:image/png;base64,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)
- 3 x 2 = 3 x (2 + 2) = (3 x 2) + (3 x 2)
- 2 x 6 = 2 x (2 + 4) = (2 x 2) + (2 x 4)
- 3 x 6 = 3 x (4 + 4) = (3 x 4) + (3 x 4)
- 3 x 6 = 3 x (2 + 4) = (3 x 2) + (3 x 4)
Hint:
We are given a figure. It is made up from small circles of same size. There are two colors, blue and green. We have to find the total area of the figure.
The correct answer is: 3 x 6 = 3 x (2 + 4) = (3 x 2) + (3 x 4)
We will consider rows and columns.
There are total 3 rows and 6 columns of the circles.
There are two different colors for the column.
We will consider one circles as one unit.
There are 6 units for a row. And, there are three units for a column.
From that 6 units have two colors, 2 for blue and 4 for green.
Area = number of columns × number of rows
= 6 × 3
= 3 × (2 + 4)
Area of blue circles = number of columns × number of rows
= 2 × 3
Area of green circles = number of columns × number of rows
= 4 × 3
Area = Area of blue circles + Area of green circles
6 × 3 = 2 × 3 + 4 × 3
3 × 6 = 3 × (2 + 4) = 2 × 3 + 4 × 3
For such questions, we should know distributive property.
Related Questions to study
An ice cream store can make 280 quarts of ice cream in 7 hours. ____________ quarts of ice cream can be made in 48 hours.
We should be careful about the units. Before operation we should make sure same quantities have same unit.
An ice cream store can make 280 quarts of ice cream in 7 hours. ____________ quarts of ice cream can be made in 48 hours.
We should be careful about the units. Before operation we should make sure same quantities have same unit.
Write the equivalent expressions for the following:
10(m + 10)
For such questions, we should the properties required to solve algebraic expression.
Write the equivalent expressions for the following:
10(m + 10)
For such questions, we should the properties required to solve algebraic expression.
400 inch is _____% of 1600 inches.
400 inch is _____% of 1600 inches.
The temperature at which a substance fuses is called its _____.
The temperature at which a substance fuses is called its _____.
The rays which are hardest to stop are________ rays.
The rays which are hardest to stop are________ rays.
A wave
on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave is
A wave
on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave is
If the velocity of planet is given by then
If the velocity of planet is given by then
The displacement for a particle performing S.H.M. is given by
. If the initial position of the particle is Icm and its initial vebocity is p cms1, then what will be itsinitial phase? The, angular frequency of the particle is ps1
The displacement for a particle performing S.H.M. is given by
. If the initial position of the particle is Icm and its initial vebocity is p cms1, then what will be itsinitial phase? The, angular frequency of the particle is ps1
As shown in figure, a spring attached to the ground vertically has a horizontal massless plate with a
mass in it. When the spring ( massless) is pressed slightly and released, the 2 kg mass, starts executing S.H.M. The force constant of the spring is
. For what minimum value of amplitude, will the mass loose contact with the plate? (Take g=10
)
![](data:image/png;base64,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)
As shown in figure, a spring attached to the ground vertically has a horizontal massless plate with a
mass in it. When the spring ( massless) is pressed slightly and released, the 2 kg mass, starts executing S.H.M. The force constant of the spring is
. For what minimum value of amplitude, will the mass loose contact with the plate? (Take g=10
)
![](data:image/png;base64,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)
A plane mirror is placed at the bottom of a tank containing a liquid of refractive index n. P is a small object at a height h above the mirror. An observer O, vertically above P, outside the liquid sees P and its image in the mirror. The apparent distance betwecn these two wall be
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)
A plane mirror is placed at the bottom of a tank containing a liquid of refractive index n. P is a small object at a height h above the mirror. An observer O, vertically above P, outside the liquid sees P and its image in the mirror. The apparent distance betwecn these two wall be
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)
The energy dissipated in a damped oscillation
The energy dissipated in a damped oscillation
If the time period of undamped oscillation is T and that of damped oscillatin is T, then what is the relation between I&.
If the time period of undamped oscillation is T and that of damped oscillatin is T, then what is the relation between I&.