Area of Other Shapes

When we talk about the area of a shape in geometry, we refer to the amount of space inside that shape. In grade 4 math, you will learn about finding the area of various two-dimensional shapes beyond simple squares and rectangles. Let's learn about these shapes and how to calculate their area in simple terms.

Understanding the region

Before we get into specific shapes, let's recap what area means. Imagine you have a flat shape, like a piece of paper or a patch of grass. The area is the surface area of the shape that covers it. If you can paint over the entire shape, the area is the size of the painted portion.

Area of a triangle

A triangle is a three-sided shape. It can look like a mountain or a slice of pizza. To find the area of a triangle, you use a special formula:

Area = (base × height) / 2

Here, base is the length of the bottom side of the triangle, and height is how high the triangle is from the base to the vertex.

Imagine you have a triangle with a base of 8 units and a height of 5 units. Let's plug these numbers into our formula:

Area = (8 × 5) / 2 = 40 / 2 = 20 square units

So, the area of this triangle is 20 square units.

Area of parallelogram

A parallelogram is a four-sided shape in which opposite sides are parallel and equal in length. It looks like a tilted rectangle. The area of a parallelogram is the same as the area of a rectangle, and its formula is:

Area = base × height

base is a side, and height is how tall the shape is, measured straight up from the base.

Suppose you have a parallelogram with a base of 10 units and a height of 4 units. Here's how you would find the area:

Area = 10 × 4 = 40 square units

The area of this parallelogram is 40 square units.

Area of trapezium

A trapezoid (or trapezium) is a four-sided shape in which one pair of opposite sides is parallel. To find the area of a trapezoid, use this formula:

Area = (base1 + base2) × height / 2

Here, base1 and base2 are the lengths of two parallel sides, and height is the distance between them.

Suppose we have a trapezoid whose bases are 6 units and 10 units, and the height is 5 units. The area is calculated as follows:

Area = (6 + 10) × 5 / 2 = 16 × 5 / 2 = 80 / 2 = 40 square units

The area of this trapezoid is 40 square units.

Area of a circle

A circle is a perfectly round shape. Every point on the edge is the same distance from the center. To find the area of a circle, you use a special number called pi (π), which equals about 3.14. The formula for area is:

Area = π × radius × radius

radius is the distance from the center of the circle to any point on the edge.

If you have a circle with a radius of 3 units, its area is:

Area = π × 3 × 3 = 3.14 × 9 ≈ 28.26 square units

So, the area of this circle is approximately 28.26 square units.

Formula review

Here's a brief summary of the sources we discussed:

• Triangle: Area = (base × height) / 2
• Parallelogram: Area = base × height
• Trapezoid: Area = (base1 + base2) × height / 2
• Circle: Area = π × radius × radius

By understanding and practicing these simple formulas, you can easily find the area of different shapes. It is helpful to visualize each shape and see how that area fills the space.

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