Question

What is the area of this shape?

Answer 1

Using the cosine rule we can work out the length of the side opposite the indicated right angle which came to be 15mm
then the final answer came to be 163mm^2

Answer 2

To get the area of this shape you need to break it apart into 2 shapes, determine the area of each and then add them together.  If you look, there is a triangle and then a trapezoid sitting on top of that.  The formulas are...

Area of a triangle = 1/2 b * h
Area of a trapezoid = 1/2 (base 1 + base 2) * h

Let's do the triangle 1st...

The base is 18mm and the height is 12 mm.  Plug it into the formula

A= 1/2 bh
A= 1/2 18 * 12
A = 1/2(216)
A = 108 mm^2

Now the trapezoid...

You have the 2 bases labeled as 18mm and 14mm.  What's the height?  Well if you notice on the side, the height for the entire figure is labeled as 17mm.  If we subtract the height of the triangle, that will give us the height of the trapezoid,  17 - 12 = 5mm.  Lets plug our numbers into the formula.

A= 1/2(base1 + base2) * h
A = 1/2(18 + 14) * 5
A= 1/2(32) * 5
A= 16 * 5 = 80mm^2

Now we have the area of the triangle (108 mm^2) and the area of the trapezoid (80 mm^2).  If we add them together it will give us the area of the entire figure.

108 + 80 =    188 mm^2