Using Triangles to Find the Area of Trapezia

First, divide the trapezium into two triangles using one of its diagonals.

For Triangle A (with the base of $8$ cm):

• Base $b = 8$ cm
• Height $h = 5$ cm
• Area $A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 8 \times 5 = 20$ cm$^2$

For Triangle B (with the base of $12$ cm):

• Base $b = 12$ cm
• Height $h = 5$ cm
• Area $A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 12 \times 5 = 30$ cm$^2$

Add the areas of both triangles to find the total area of the trapezium: $20$ cm$^2 + 30$ cm$^2 = 50$ cm$^2$.

The total area of the trapezium is $50$ cm$^2$.

First, divide the trapezium into two triangles using one of its diagonals.

For Triangle A (with the base of $5$ cm):

• Area $A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 5 \times 6 = 15$ cm$^2$

For Triangle B (with the base of $15$ cm):

• Area $A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 15 \times 6 = 45$ cm$^2$

Add the areas of both triangles to find the total area of the trapezium: $15$ cm$^2 + 45$ cm$^2 = 60$ cm$^2$.

The total area of the trapezium is $60$ cm$^2$.

First, identify the bases and the height: $base_1 = 6$ cm, $base_2 = 10$ cm, and height = 3 cm. Substitute into the formula:

$ \text{Area} = \frac{(6 + 10)}{2} \times 3 $

Solve for the area:

$ \text{Area} = \frac{16}{2} \times 3 = 8 \times 3 = 24 \, \text{cm}^2 $

The area of the trapezium is $24$ cm$^2$.

Identify the bases and the height: $base_1 = 7$ cm, $base_2 = 12$ cm, and height = 5 cm. Substitute into the formula:

$ \text{Area} = \frac{(7 + 12)}{2} \times 5 $

Solve for the area:

$ \text{Area} = \frac{19}{2} \times 5 = 9.5 \times 5 = 47.5 \, \text{cm}^2 $

The area of the trapezium is $47.5$ cm$^2$.

Identify the bases and the height: $base_1 = 9$ cm, $base_2 = 15$ cm, and height = 6 cm. Substitute into the formula:

$ \text{Area} = \frac{(9 + 15)}{2} \times 6 $

Solve for the area:

$ \text{Area} = \frac{24}{2} \times 6 = 12 \times 6 = 72 \, \text{cm}^2 $

The area of the trapezium is $72$ cm$^2$

A parallelogram is a four-sided shape where opposite sides are parallel and equal in length, resembling a slanted rectangle.

The area of a parallelogram is found by multiplying its base by its height, where the height is perpendicular to the base.

A trapezium is a four-sided shape with at least one pair of parallel sides. These parallel sides are known as the bases of the trapezium.

The area of a trapezium can be found by averaging the lengths of the parallel sides (bases), and then multiplying by the height.

Decomposing a trapezium into triangles simplifies the calculation by breaking the shape into simpler parts, making it easier to measure the area.

Yes, the area formula for a trapezium can be applied to all trapezia, regardless of their specific shape or size.

To use the formula, you need the lengths of the two parallel sides (bases) and the perpendicular distance between them (height).

The height of a trapezium is the perpendicular distance from one base to the parallel base. It can be measured or calculated based on given information.

Understanding the area of shapes is important for solving various practical problems, including those in construction, art and design.

Knowing these areas helps in planning projects, managing space and estimating materials needed for construction or art projects.