To find the total area of the figure, we'll calculate the area of the triangle and the area of the rectangle separately, and then combine them.
Area of the Triangle: The formula for the area of a triangle is: \[ \text{Area of Triangle} = \frac{B \times H}{2} \] Here, \( B \) (the base) is given as 6 inches, and \( H \) is the height (also 6 inches).
Substituting in the values: \[ \text{Area of Triangle} = \frac{6 \times 6}{2} = \frac{36}{2} = 18 \text{ in}^2 \]
Area of the Rectangle: The formula for the area of a rectangle is: \[ \text{Area of Rectangle} = B \times H \] Here, \( B \) is 11 inches and \( H \) is 6 inches.
Substituting in the values: \[ \text{Area of Rectangle} = 11 \times 6 = 66 \text{ in}^2 \]
Total Area: Now we add the areas of the triangle and rectangle together: \[ \text{Total Area} = \text{Area of Triangle} + \text{Area of Rectangle} \] \[ \text{Total Area} = 18 \text{ in}^2 + 66 \text{ in}^2 = 84 \text{ in}^2 \]
Thus, the total area of the figure is: \[ A = 84 \text{ in}^2 \]