Question

the figure is made up of 3 identical equilateral triangles (a) find the length of ab (b) find the perimeter of the shaded parts

Explanation:

Step1: Find side - length of equilateral triangle

Let the side - length of each equilateral triangle be $x$ cm.
From the figure, we can see that $2x - 3=18$.
Solve for $x$:
$2x=18 + 3$
$2x=21$
$x = 10.5$ cm.

Step2: Answer part (a)

In an equilateral triangle, all sides are equal. So, the length of $AB$ is the side - length of an equilateral triangle, $AB = 10.5$ cm.

Step3: Analyze the perimeter of the shaded parts

For the perimeter of the shaded parts, we note that the outer sides of the shaded regions are considered.
The perimeter of the shaded parts consists of 4 side - lengths of the equilateral triangles.
Since the side - length of each equilateral triangle $x = 10.5$ cm, the perimeter of the shaded parts $P=4x$.
$P = 4\times10.5=42$ cm.

Answer:

(a) $10.5$ cm
(b) $42$ cm