To answer this question, we need to divide the previous figure into two known figures to calculate the total area. We have that figure 1 is a rectangle with sides 15mm and 30mm, and figure 2 is a right triangle with height equal to one of its sides (h = 15mm), and base equal to the other side (b = 10mm).
Now, we can calculate the area of figure 1 (rectangle) and figure 2 (triangle), using the corresponding formulas:
Area of the Rectangle
[tex]A_{\text{rectangle}}=w\cdot l=15\operatorname{mm}\cdot30mm=450\operatorname{mm}^2[/tex]
Area of the Triangle
[tex]A_{\text{triangle}}=\frac{b\cdot h}{2}=\frac{10\operatorname{mm}\cdot(15\operatorname{mm}+15\operatorname{mm})}{2}=\frac{10\operatorname{mm}\cdot30\operatorname{mm}}{2}=\frac{300\operatorname{mm}^2}{2}[/tex]
Thus
[tex]A_{\text{triangle}}=150\operatorname{mm}^2[/tex]
Now, the total area is:
[tex]A_{\text{rectangle}}+A_{\text{triangle}}=450\operatorname{mm}+150\operatorname{mm}=600\operatorname{mm}^2[/tex]
Therefore, the total area is equal to 600 sq. millimeters.
