Hi Simon. Yes, for the top shape, find the height of one triangle (they're both the same). These two exercises don't require trigonometry. Are you taking a trig class? The shapes involved have simple area formulas. I'll use those formulas.
The top shape is a rectangle. Its base measures 12, and you need to calculate its height (to use in the area formula below).
The height of the rectangle is the same as the height of each right triangle. Use the
Pythagorean Theorem to find the height.
Rectangle Area = Base * Height
(The asterisk is a multiplication sign)
Not this time. We can extend the side labeled 10, to divide the bottom shape into a rectangle and a right triangle. We can add those two areas.
View attachment 28728
Triangle Area = 1/2 * Base * Height
The order of steps is:
1) Get the value of x from looking at the diagram
2) Calculate the value of y from x+y=20
3) Calculate the triangle height (green) using Pythagorean Theorem
4) Use the green side, to calculate the rectangle's other dimension
5) Calculate the rectangle area by formula
6) Calculate the triangle area by formula
7) Combine those two areas, to get the total area
If you get stuck, please show what you tried.
?