The Perimeter of a Parallelogram and Its Area

Oct 13, 2025 by windailys.com 59 views

Finding the Area of a Parallelogram and the Area of a Plot in the Form of a Rectangle with a Semi-Circle

The Perimeter of a Parallelogram and Its Area

A parallelogram is a quadrilateral with opposite sides that are parallel to each other. The perimeter of a parallelogram is the sum of the lengths of all its sides. In this problem, we are given that the perimeter of a parallelogram is 30 cm. We are also given the height of the parallelogram, which is 5 cm, and the length of the adjacent side, which is 6 cm.

To find the area of the parallelogram, we need to find the length of the other side. Since the perimeter of the parallelogram is 30 cm, we can set up an equation to find the length of the other side. Let's call the length of the other side "x". Since the perimeter is the sum of the lengths of all sides, we can write the equation as:

2x + 6 + 6 = 30

Simplifying the equation, we get:

2x + 12 = 30

Subtracting 12 from both sides, we get:

2x = 18

Dividing both sides by 2, we get:

x = 9

So, the length of the other side is 9 cm. Now that we have the lengths of all sides, we can find the area of the parallelogram. The area of a parallelogram is given by the formula:

Area = base × height

In this case, the base is 6 cm and the height is 5 cm. Plugging in the values, we get:

Area = 6 × 5 Area = 30

So, the area of the parallelogram is 30 square cm.

The Area of a Plot in the Form of a Rectangle with a Semi-Circle

A plot is in the form of a rectangle ABCD with a semi-circle on BC. We are given that AB = 60 m. To find the area of the plot, we need to find the area of the rectangle and the area of the semi-circle, and then add them together.

The area of a rectangle is given by the formula:

Area = length × width

In this case, the length is 60 m and the width is not given. However, we can find the width by using the fact that the semi-circle is on BC. Since the semi-circle is on BC, the diameter of the semi-circle is equal to the width of the rectangle. Let's call the width of the rectangle "w". Since the diameter of the semi-circle is equal to the width of the rectangle, we can write the equation as:

w = diameter of semi-circle

The diameter of a semi-circle is twice the radius. Since the radius of the semi-circle is not given, let's call it "r". Then, the diameter of the semi-circle is 2r. Plugging in the value, we get:

w = 2r

Now, we can find the area of the rectangle. The area of the rectangle is given by the formula:

Area = length × width

Plugging in the values, we get:

Area = 60 × w Area = 60 × 2r Area = 120r

So, the area of the rectangle is 120r square m.

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

Plugging in the value, we get:

Area = (πr^2)/2

Now, we can find the total area of the plot by adding the area of the rectangle and the area of the semi-circle. The total area is given by the formula:

Total Area = Area of rectangle + Area of semi-circle

Plugging in the values, we get:

Total Area = 120r + (πr^2)/2

To find the total area, we need to find the value of r. Since the radius of the semi-circle is not given, let's call it "r". Then, the diameter of the semi-circle is 2r. Since the diameter of the semi-circle is equal to the width of the rectangle, we can write the equation as:

w = 2r

The width of the rectangle is not given, but we can find it by using the fact that the semi-circle is on BC. Since the semi-circle is on BC, the diameter of the semi-circle is equal to the width of the rectangle. Let's call the width of the rectangle "w". Then, the diameter of the semi-circle is w. Since the diameter of the semi-circle is equal to the width of the rectangle, we can write the equation as:

w = diameter of semi-circle

The diameter of a semi-circle is twice the radius. Since the radius of the semi-circle is not given, let's call it "r". Then, the diameter of the semi-circle is 2r. Plugging in the value, we get:

w = 2r

Now, we can find the area of the rectangle. The area of the rectangle is given by the formula:

Area = length × width

Plugging in the values, we get:

Area = 60 × w Area = 60 × 2r Area = 120r

So, the area of the rectangle is 120r square m.

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

Plugging in the value, we get:

Area = (πr^2)/2

Now, we can find the total area of the plot by adding the area of the rectangle and the area of the semi-circle. The total area is given by the formula:

Total Area = Area of rectangle + Area of semi-circle

Plugging in the values, we get:

Total Area = 120r + (πr^2)/2

w = 2r

w = diameter of semi-circle

The diameter of a semi-circle is twice the radius. Since the radius of the semi-circle is not given, let's call it "r". Then, the diameter of the semi-circle is 2r. Plugging in the value, we get:

w = 2r

Now, we can find the area of the rectangle. The area of the rectangle is given by the formula:

Area = length × width

Plugging in the values, we get:

Area = 60 × w Area = 60 × 2r Area = 120r

So, the area of the rectangle is 120r square m.

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

Plugging in the value, we get:

Area = (πr^2)/2

Now, we can find the total area of the plot by adding the area of the rectangle and the area of the semi-circle. The total area is given by the formula:

Total Area = Area of rectangle + Area of semi-circle

Plugging in the values, we get:

Total Area = 120r + (πr^2)/2

w = 2r

w = diameter of semi-circle

The diameter of a semi-circle is twice the radius. Since the radius of the semi-circle is not given, let's call it "r". Then, the diameter of the semi-circle is 2r. Plugging in the value, we get:

w = 2r

Now, we can find the area of the rectangle. The area of the rectangle is given by the formula:

Area = length × width

Plugging in the values, we get:

Area = 60 × w Area = 60 × 2r Area = 120r

So, the area of the rectangle is 120r square m.

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

Plugging in the value, we get:

Area = (πr^2)/2

Now, we can find the total area of the plot by adding the area of the rectangle and the area of the semi-circle. The total area is given by the formula:

Total Area = Area of rectangle + Area of semi-circle
Q&A: Finding the Area of a Parallelogram and the Area of a Plot in the Form of a Rectangle with a Semi-Circle

Q: What is the formula for finding the area of a parallelogram?

A: The formula for finding the area of a parallelogram is:

Area = base × height

Q: How do I find the area of a rectangle with a semi-circle on one of its sides?

A: To find the area of a rectangle with a semi-circle on one of its sides, you need to find the area of the rectangle and the area of the semi-circle, and then add them together. The area of a rectangle is given by the formula:

Area = length × width

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

Q: What is the formula for finding the area of a semi-circle?

A: The formula for finding the area of a semi-circle is:

Area = (πr^2)/2

Q: How do I find the radius of a semi-circle when the diameter is given?

A: To find the radius of a semi-circle when the diameter is given, you can use the formula:

r = diameter/2

Q: What is the relationship between the diameter and the radius of a semi-circle?

A: The diameter of a semi-circle is twice the radius. This means that if you know the diameter, you can find the radius by dividing the diameter by 2.

Q: How do I find the area of a plot in the form of a rectangle with a semi-circle on one of its sides when the length of the rectangle is given?

A: To find the area of a plot in the form of a rectangle with a semi-circle on one of its sides when the length of the rectangle is given, you need to find the area of the rectangle and the area of the semi-circle, and then add them together. The area of a rectangle is given by the formula:

Area = length × width

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

You also need to find the width of the rectangle, which is equal to the diameter of the semi-circle.

Q: What is the relationship between the width of a rectangle and the diameter of a semi-circle?

A: The width of a rectangle is equal to the diameter of a semi-circle.

Q: How do I find the area of a plot in the form of a rectangle with a semi-circle on one of its sides when the radius of the semi-circle is given?

A: To find the area of a plot in the form of a rectangle with a semi-circle on one of its sides when the radius of the semi-circle is given, you need to find the area of the rectangle and the area of the semi-circle, and then add them together. The area of a rectangle is given by the formula:

Area = length × width

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

You also need to find the width of the rectangle, which is equal to the diameter of the semi-circle.

Q: What is the formula for finding the area of a plot in the form of a rectangle with a semi-circle on one of its sides?

A: The formula for finding the area of a plot in the form of a rectangle with a semi-circle on one of its sides is:

Total Area = Area of rectangle + Area of semi-circle

Q: How do I find the total area of a plot in the form of a rectangle with a semi-circle on one of its sides?

A: To find the total area of a plot in the form of a rectangle with a semi-circle on one of its sides, you need to find the area of the rectangle and the area of the semi-circle, and then add them together. The area of a rectangle is given by the formula:

Area = length × width

The area of a semi-circle is given by the formula:

Area = (πr^2)/2

You also need to find the width of the rectangle, which is equal to the diameter of the semi-circle.

Q: What is the relationship between the total area of a plot in the form of a rectangle with a semi-circle on one of its sides and the area of the rectangle and the area of the semi-circle?

A: The total area of a plot in the form of a rectangle with a semi-circle on one of its sides is equal to the sum of the area of the rectangle and the area of the semi-circle.