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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.

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.

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.

The line of symmetry of a semicircle is the vertical line that passes through its center, perpendicular to the base (the diameter). This line divides the semicircle into two mirror-image halves.

Yes, a semicircle does have rotational symmetry, but its order is 1, meaning that it only matches its original shape in one orientation through a full 360-degree rotation. However, if we consider the concept of rotational symmetry in the context of being able to rotate an object less than a full circle (360 degrees) and have it appear the same, then a semicircle exhibits rotational symmetry of order 2 when rotated 180 degrees around the midpoint of its diameter. This is because flipping it 180 degrees around this point will present the same shape and orientation due to its symmetrical nature.

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

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.

First, let's find the area of one marble tile:

Area of one tile = Length × Width = 10 cm × 12 cm = 120 cm²

Now, we need to convert the area from square centimeters to square meters since the wall size is given in meters.

1 square meter = 10,000 square centimeters

So, 120 cm² = 120 / 10,000 m² = 0.012 m²

Next, let's find the area of the wall:

Area of the wall = Length × Width = 3 m × 4 m = 12 m²

Now, to find out how many tiles are needed, we divide the total area of the wall by the area of one tile:

Number of tiles = Area of the wall / Area of one tile = 12 m² / 0.012 m² = 1000 tiles

Therefore, 1000 marble tiles will be required to cover the wall.

Now, let's find the total cost of the tiles at the rate of Rs 2 per tile:

Total cost = Number of tiles × Cost per tile = 1000 tiles × Rs 2 per tile = Rs 2000

So, the total cost of the tiles will be Rs 2000.

First, let's convert the dimensions of the table top into centimeters, since the rate given is in paise per square centimeter:

Length of the table top = 9 dm * 10 cm/dm + 5 cm = 90 cm + 5 cm = 95 cm Breadth of the table top = 6 dm * 10 cm/dm + 5 cm = 60 cm + 5 cm = 65 cm

Now, let's calculate the area of the table top:

Area of the table top = Length × Breadth = 95 cm × 65 cm = 6175 cm²

Now, let's find the cost to polish the table top at the rate of 20 paise per square centimeter:

Cost = Area of the table top × Rate = 6175 cm² × 20 paise/cm² = 123500 paise

Since 100 paise = 1 rupee, we divide by 100 to convert paise to rupees:

Cost = 123500 paise / 100 = Rs. 1235

So, the cost to polish the table top will be Rs. 1235.

First, let's find the area of one tile:

Area of one tile = Length × Width = 22 cm × 10 cm = 220 cm²

Now, we need to convert the area of one tile from square centimeters to square meters since the room dimensions are given in meters.

1 square meter = 10,000 square centimeters

So, 220 cm² = 220 / 10,000 m² = 0.022 m²

Next, let's find the area of the room:

Area of the room = Length × Width = 9.68 m × 6.2 m = 59.936 m² (approximately)

Now, let's find how many tiles are needed to cover the floor of the room:

Number of tiles = Area of the room / Area of one tile = 59.936 m² / 0.022 m² ≈ 2724 tiles

Now, let's find the total cost of the tiles at the rate of Rs 2.50 per tile:

Total cost = Number of tiles × Cost per tile = 2724 tiles × Rs 2.50 per tile = Rs 6810

So, the total cost of the tiles will be Rs 6810.