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For an isosceles triangle, the line of symmetry can also be referred to as the "axis of symmetry." This line divides the triangle into two mirror-image parts, running from the apex (the vertex opposite the base) to the midpoint of the base. read more

For an isosceles triangle, the line of symmetry can also be referred to as the "axis of symmetry." This line divides the triangle into two mirror-image parts, running from the apex (the vertex opposite the base) to the midpoint of the base.

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Shapes with no line of symmetry do not divide into two mirror-image halves, regardless of how you try to fold or bisect them. Here are three examples: Scalene Triangle: A triangle with all sides of different lengths and all angles of different sizes has no line of symmetry because there... read more

Shapes with no line of symmetry do not divide into two mirror-image halves, regardless of how you try to fold or bisect them. Here are three examples:

1. Scalene Triangle: A triangle with all sides of different lengths and all angles of different sizes has no line of symmetry because there is no way to divide it into two parts that are mirror images of each other.

2. Irregular Polygon: An irregular polygon, which does not have equal-length sides or equal angles, typically has no line of symmetry. An example would be a five-sided polygon where no two sides or angles are the same.

3. Parallelogram (excluding rectangles and rhombuses): A general parallelogram (which is not a rectangle or rhombus) has no lines of symmetry. Its opposite sides are equal in length, and opposite angles are equal, but it does not fold into two parts that are mirror images of each other unless it is a special type like a rectangle or rhombus, which do have lines of symmetry.

These shapes illustrate that symmetry is not a universal characteristic of all geometric figures.

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An example of a geometrical figure that has neither a line of symmetry nor rotational symmetry is a scalene triangle. A scalene triangle is defined by having all three sides of different lengths and all three internal angles of different measures. This lack of uniformity means it cannot be divided... read more

An example of a geometrical figure that has neither a line of symmetry nor rotational symmetry is a scalene triangle. A scalene triangle is defined by having all three sides of different lengths and all three internal angles of different measures. This lack of uniformity means it cannot be divided into two mirror-image halves by any line (i.e., it has no line of symmetry). Additionally, it cannot be rotated around its center to a position where it looks exactly the same as its original position (i.e., it has no rotational symmetry), except at rotations of 360°, which applies to all figures as a return to the original orientation and is generally not considered when discussing rotational symmetry.

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An example of a letter in the English alphabet that has no line of symmetry is the letter "F". The letter "F" does not have a line through which it can be divided into two mirror-image halves, either horizontally or vertically. read more

An example of a letter in the English alphabet that has no line of symmetry is the letter "F". The letter "F" does not have a line through which it can be divided into two mirror-image halves, either horizontally or vertically.

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The letter "Z" has rotational symmetry of order 2. This means that if you rotate the letter "Z" by 180 degrees, it appears the same as its original orientation. read more

The letter "Z" has rotational symmetry of order 2. This means that if you rotate the letter "Z" by 180 degrees, it appears the same as its original orientation.

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To find the area of a square with a side length of 16.5 decameters (dam) in square meters: Area = side^2 = (16.5 dam)^2 = 16.5^2 dam^2 = 272.25 m^2 So, the area of the square is 272.25 square meters. read more

To find the area of a square with a side length of 16.5 decameters (dam) in square meters:

Area = side^2 = (16.5 dam)^2 = 16.5^2 dam^2 = 272.25 m^2

So, the area of the square is 272.25 square meters.

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To find the area of a rectangular field in acres with sides of 200 meters and 125 meters: Then, we convert the area from square meters to acres. Since 1 acre is equal to 4046.86 square meters: So, the area of the rectangular field is approximately 6.18 acres. read more

To find the area of a rectangular field in acres with sides of 200 meters and 125 meters:

$\dpi{100}&space;$&space;\text{Area}&space;=&space;\text{length}&space;\times&space;\text{width}&space;=&space;200&space;\,&space;\text{m}&space;\times&space;125&space;\,&space;\text{m}&space;=&space;25,000&space;\,&space;\text{m}^2&space;$&space;$&space;\text{Area&space;in&space;acres}&space;=&space;\frac{25,000&space;\,&space;\text{m}^2}{4046.86&space;\,&space;\text{m}^2/\text{acre}}&space;\approx&space;6.18&space;\,&space;\text{acres}&space;$$

Then, we convert the area from square meters to acres. Since 1 acre is equal to 4046.86 square meters:

So, the area of the rectangular field is approximately 6.18 acres.

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To find the cost of painting the wall, we first need to calculate the area of the wall excluding the area covered by the door, and then multiply it by the cost per square meter. Calculate the cost: Cost per square meter = Rs 2.50Total cost = Area of the wall excluding the door × Cost per square... read more

To find the cost of painting the wall, we first need to calculate the area of the wall excluding the area covered by the door, and then multiply it by the cost per square meter.$\dpi{100}&space;-&space;Total&space;area&space;of&space;the&space;wall&space;=&space;$$10&space;\,&space;\text{m}&space;\times&space;10&space;\,&space;\text{m}&space;=&space;100&space;\,&space;\text{m}^2$$&space;-&space;Area&space;covered&space;by&space;the&space;door&space;=&space;$$3&space;\,&space;\text{m}&space;\times&space;2&space;\,&space;\text{m}&space;=&space;6&space;\,&space;\text{m}^2$$&space;-&space;Area&space;of&space;the&space;wall&space;excluding&space;the&space;door&space;=&space;$$100&space;\,&space;\text{m}^2&space;-&space;6&space;\,&space;\text{m}^2&space;=&space;94&space;\,&space;\text{m}^2$$$

Calculate the cost:

• Cost per square meter = Rs 2.50
Total cost = Area of the wall excluding the door × Cost per square meter
$\dpi{100}&space;-&space;Total&space;cost&space;=&space;$$94&space;\,&space;\text{m}^2&space;\times&space;Rs&space;\,&space;2.50/\text{m}^2$$&space;-&space;Total&space;cost&space;=&space;Rs&space;235$

So, the cost of painting the wall is Rs 235.

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First, let's find the perimeter of the rectangle, which is equal to the length of the wire: Perimeter of the rectangle = 2 * (length + breadth) = 2 * (40 cm + 22 cm) = 2 * 62 cm = 124 cm Since the wire is bent to form a square, the perimeter of the square will also be 124 cm. Now, let's find... read more

First, let's find the perimeter of the rectangle, which is equal to the length of the wire:

Perimeter of the rectangle = 2 * (length + breadth) = 2 * (40 cm + 22 cm) = 2 * 62 cm = 124 cm

Since the wire is bent to form a square, the perimeter of the square will also be 124 cm.

Now, let's find the measure of each side of the square:

Perimeter of the square = 4 * side

So, 4 * side = 124 cm

Dividing both sides by 4:

side = 124 cm / 4 = 31 cm

Each side of the square will measure 31 cm.

Now, let's find the area enclosed by each shape:

Area of the rectangle = length * breadth = 40 cm * 22 cm = 880 cm²

Area of the square = side * side = 31 cm * 31 cm = 961 cm²

Comparing the two areas, we find that the square encloses more area than the rectangle.

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To find the total area of glass required for 12 panes, we first find the area of one pane and then multiply it by the number of panes. Area of one pane = Length × Breadth = 25 cm × 16 cm = 400 cm² Now, we have to convert the area from square centimeters to square meters,... read more

To find the total area of glass required for 12 panes, we first find the area of one pane and then multiply it by the number of panes.

Area of one pane = Length × Breadth = 25 cm × 16 cm = 400 cm²

Now, we have to convert the area from square centimeters to square meters, as 1 square meter equals 10,000 square centimeters.

So, 400 cm² = 400 / 10,000 m² ≈ 0.04 m²

Therefore, the area of one pane is approximately 0.04 square meters.

To find the total area required for 12 panes, we multiply the area of one pane by the number of panes:

Total area = Area of one pane × Number of panes = 0.04 m² × 12 = 0.48 m²

So, 0.48 square meters of glass will be required for 12 panes.

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