Area and Perimeter Grade 9: Square, rhombus, parallelogram, rectangle

Summary

In this lesson, the instructor explains the concepts of perimeter and area for four shapes: square, rectangle, rhombus, and parallelogram. The perimeter is described as the total distance around the shape, while the area covers the space inside. Step-by-step examples are provided for calculating perimeter and area using simple multiplication and understanding the properties of each shape. Special attention is given to the difference between perpendicular and slanted sides when calculating the area of shapes like rhombuses and parallelograms, emphasizing the importance of 90-degree angles in these calculations.

Takeaways

• 📏 Perimeter is the total distance around the outside of a shape, calculated by adding all sides together.
• 🔢 In a square, all four sides are equal, so the perimeter is the side length multiplied by 4.
• 🌍 Area represents the space inside a shape and is calculated differently depending on the shape.
• 🟦 For a square, the area is found by multiplying the length of one side by itself (side × side).
• 🧮 A rectangle’s perimeter is calculated by adding the lengths of all sides, or by multiplying each pair of opposite sides and summing them.
• 🔳 The area of a rectangle is calculated by multiplying its length and width.
• 🔷 A rhombus has all sides equal, but its area is determined by multiplying the base by the height (not the side length).
• 📐 The height of a rhombus or parallelogram is always the perpendicular distance from the top to the base, not the slanted side.
• ➗ For a parallelogram, the area is found by multiplying the base by the perpendicular height.
• 📝 Always ensure that the area calculations use dimensions that form a 90-degree angle for accurate results.

Q & A

What is the perimeter of a shape?

The perimeter of a shape is the total distance around the outside of the shape. It can be found by adding up the lengths of all the sides.

How do you calculate the area of a square?

To calculate the area of a square, you multiply the length of one side by itself (side × side). For example, if one side is 3 units, the area would be 3 × 3 = 9 square units.

What is the difference between perimeter and area?

The perimeter is the distance around the outside of a shape, while the area is the amount of space inside the shape.

How do you find the perimeter of a rectangle?

To find the perimeter of a rectangle, add the lengths of all four sides. Alternatively, you can use the formula: 2 × (length + width).

Why can’t you use the side lengths directly to find the area of a rhombus?

You can’t use the side lengths directly to find the area of a rhombus because it is a tilted shape. You need to use the base and the height (which forms a 90-degree angle with the base) to calculate the area.

What formula do you use to find the area of a rhombus?

To find the area of a rhombus, use the formula: base × height, where the height is the perpendicular distance from the base to the top.

How do you calculate the area of a rectangle?

To calculate the area of a rectangle, multiply the length by the width (length × width).

What is special about the sides of a rhombus?

All four sides of a rhombus are equal in length.

What is the height in a parallelogram, and how is it used to find the area?

The height in a parallelogram is the perpendicular distance from the top of the shape to the base. To find the area, multiply the base by the height (base × height).

What is the key concept to remember when finding the area of slanted shapes like a rhombus or parallelogram?

When finding the area of slanted shapes like a rhombus or parallelogram, always use the height, which forms a 90-degree angle with the base, instead of the slanted side lengths.