Construct an equilateral triangle in a circle of radius 4cm. Explain the steps.

Using a ruler, measure $4 \text{ cm}$. Set your compass to this radius. Draw a circle with any center point O.

Mark any point A on the circumference of the circle. With A as the center and the same radius ($4 \text{ cm}$), draw an arc that intersects the circle at two points. Let's call one of these intersection points B.

With B as the center and the same radius ($4 \text{ cm}$), draw another arc that intersects the circle at a new point. Let's call this point C.

Connect points A, C, and the point diametrically opposite to B (which would be the third vertex if you continued marking points around the circle, or simply connect A, C, and the point that is two compass-widths away from A in the other direction).
A more direct method:

1. Draw a circle with center O and radius $4 \text{ cm}$.
2. Draw a diameter through O, marking points P and Q on the circumference.
3. With P as the center and radius $4 \text{ cm}$, draw an arc that intersects the circle at two points, say R and S.
4. Connect points Q, R, and S. Triangle QRS is an equilateral triangle inscribed in the circle.

b) What is the length of the triangle?

For an equilateral triangle inscribed in a circle with radius $R$, the side length $s$ is given by the formula:

Given radius $R = 4 \text{ cm}$.

Using $\sqrt{3} \approx 1.732$:

The length of the side of the equilateral triangle is $\boxed{4\sqrt{3} \text{ cm}}$.

:
Study the figure below and answer the questions that follow.
The figure is a trapezium with parallel sides of $14 \text{ m}$ and $26 \text{ m}$, and a height of $8 \text{ m}$.

a) Find the area of the figure.

The lengths of the parallel sides are $a = 14 \text{ m}$ and $b = 26 \text{ m}$.
The height of the trapezium is $h = 8 \text{ m}$.

The area of a trapezium is given by the formula:

The area of the figure is $\boxed{\text{160 m}^2}$.