Determine the area of the figure below to the nearest 3 decimal places using Heron's formula.
Heron's formula for the area of a triangle with sides , , and is
where is the semi-perimeter of the triangle, given by .
To find the area of this shape, we calculate the area of the triangle and the rectangle. Firstly, we apply Heron's formula to calculate the area of the triangle. We start by finding the semi-perimeter .
From this, we can calculate the area of the triangle.
The total area of the shape is the sum of the area of the triangle and the area of the rectangle. Hence,