Learn Maths with Free Lessons & Tips

The difference between a triangle and a triangular region lies in their definitions and conceptualizations:

1. Triangle:

   • A triangle is a geometric figure formed by three line segments called sides, and three angles.
   • It is defined by connecting three non-collinear points in a plane.
   • Each side of the triangle connects two vertices, and each vertex is a point where two sides intersect.
   • A triangle is a two-dimensional shape with no interior space.

2. Triangular Region:

   • The triangular region refers to the interior space enclosed by the sides of a triangle.
   • It is the area bounded by the three sides of the triangle.
   • The triangular region is the two-dimensional space within the triangle itself.
   • It includes all the points that lie inside the triangle, including the area enclosed by the sides and the vertices of the triangle.

In summary, a triangle is the geometric figure formed by three line segments, while the triangular region is the area enclosed by those line segments within the triangle. The triangle itself represents the boundaries of the triangular region.

To draw triangle DEF with side lengths DE = DF = 4 cm and EF = 6 cm, follow these steps:

1. Draw a line segment of length 6 cm. This will represent side EF.

2. At one end of the line segment, mark point F.

3. With F as the center and a radius of 4 cm, draw an arc to intersect the line segment EF. Mark this point as D.

4. Now, with F as the center and a radius of 4 cm, draw another arc to intersect the line segment EF. Mark this point as E.

5. Connect points D, E, and F to form triangle DEF.

Now, to measure angles E and F, you can use a protractor:

• Measure angle E: Place the center of the protractor at point E, align the baseline of the protractor along side DE, and read the angle where side EF intersects the protractor.

• Measure angle F: Place the center of the protractor at point F, align the baseline of the protractor along side EF, and read the angle where side DE intersects the protractor.

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.

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.

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.