Answer:
[tex]67.5\text{ [square units]}[/tex]
Step-by-step explanation:
The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.
Formulas:
- Area of rectangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=bh[/tex]
- Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]
By definition, the base and height must intersect at a 90 degree angle.
The rectangle has a base of 10 and a height of 5. Therefore, its area is [tex]A=10\cdot 5=50[/tex].
The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 2\cdot 5=5[/tex].
Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 5\cdot 5=12.5[/tex].
Thus, the area of the total irregular figure is:
[tex]50+5+12.5=\boxed{67.5\text{ [square units]}}[/tex]
