Areas & Perimeter of Rectangles and Rectilinear Shapes

Summary

This video explains how to calculate the area and perimeter of rectangles and other rectilinear shapes. It covers the key formulas for area (width × height) and perimeter (2 × (width + height)) with examples, including calculating the area of a rectangle, finding the height given the area, and solving real-life problems like determining the cost of paving a path around a pond. The video also demonstrates how to handle more complex shapes by splitting them into simpler rectangles and applying the same principles to find their area and perimeter.

Takeaways

• 😀 The area of a rectangle is calculated by multiplying its width by its height.
• 😀 The perimeter of a rectangle is the total length of all its sides, which can be found by adding up the lengths of all four sides.
• 😀 When finding the area of a complex shape, you can subtract the area of a smaller shape (e.g., a pond) from the area of a larger shape (e.g., a surrounding path).
• 😀 The cost of paving a path can be calculated by determining the area of the path and dividing it by the area covered by a single paving stone, then multiplying by the cost per unit.
• 😀 To find the missing dimension (height) of a rectangle when the area is known, divide the area by the known width.
• 😀 When calculating the perimeter of a rectangle, subtract the known side lengths from the total perimeter and divide the remainder to find the length of the unknown sides.
• 😀 The area of a rectilinear shape (with right angles) can be split into smaller rectangles to simplify calculations.
• 😀 In an L-shaped figure, the perimeter can be determined by converting it into a rectangle and using the same perimeter formula.
• 😀 To calculate the perimeter of a complex shape, you can sum the lengths of all outer edges or use shortcuts like treating parts of the shape as rectangles.
• 😀 The area of a complex shape can be found by dividing it into simpler sections, calculating the area of each section, and then adding them together.

Q & A

What is the formula for calculating the area of a rectangle?

The area of a rectangle is calculated by multiplying the width by the height. The formula is: Area = Width × Height.

How is the perimeter of a rectangle calculated?

The perimeter of a rectangle is calculated by adding together the lengths of all four sides. The formula is: Perimeter = 2 × (Width + Height).

In the first example, what is the area of a rectangle with width 4 meters and height 3 meters?

The area of the rectangle is 12 square meters, calculated as: Area = 4 × 3 = 12 square meters.

What is the total perimeter of a rectangle with width 4 meters and height 3 meters?

The perimeter of the rectangle is 14 meters, calculated as: Perimeter = 4 + 3 + 4 + 3 = 14 meters.

How do you calculate the cost of paving a path around a pond?

To calculate the cost of paving, first find the area of the path by subtracting the area of the pond from the total area of the larger rectangle. Then, divide the total area of the path by the area covered by one lot of paving stones and multiply by the cost per lot.

What is the total area of the path around a pond that is 8 meters by 3 meters, with a 2-meter-wide path all around?

The total area of the path is 60 square meters. First, find the total area of the larger rectangle (12 meters by 7 meters = 84 square meters) and subtract the area of the pond (3 meters by 8 meters = 24 square meters). So, 84 - 24 = 60 square meters.

If the cost for paving is £20 per 5 meters squared, how much does it cost to pave a path of 60 square meters?

The cost to pave 60 square meters is £240. This is calculated by dividing the area of the path (60 square meters) by 5 to get 12 lots of paving stones, then multiplying by the cost per lot: 12 × £20 = £240.

How can you find the height of a rectangle when given the area and width?

To find the height, divide the area by the width. For example, if the area is 28.35 square meters and the width is 4.2 meters, the height is 28.35 ÷ 4.2 = 6.75 meters.

If the perimeter of a rectangle is given as 20 meters and the width is 4.2 meters, how do you find the height?

First, subtract the lengths of the two known sides from the perimeter: 20 meters - 2 × 4.2 meters = 11.6 meters. Then, divide the remaining length by 2 to find the height: 11.6 ÷ 2 = 5.8 meters.

How do you calculate the perimeter of a complex L-shaped rectilinear shape?

To calculate the perimeter of an L-shaped shape, identify the lengths of the outer sides. You can often replace parts of the shape with equivalent lengths from other sides and add them together. In the example, the perimeter is 46 centimeters, calculated by adding the lengths of all outer sides: 12 + 11 + 4 + 4 + 8 + 7 = 46 centimeters.