Answer:
67.5 cm²
Step-by-step explanation:
The figure can be decomposed into figures whose area formulas you know.
Decomposition
As the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.
Trapezoid
The area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the parallel bases, and h is the height.
The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...
A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²
Rectangle
The area of a rectangle is given by the formula ...
A = LW
where L and W represent the length and width, respectively.
The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...
A = (15 cm)(3 cm) = 45 cm²
Total area
The total area of the figure is the sum of the areas of the trapezoid and rectangle:
A = (22.5 cm²) + (45 cm²) = 67.5 cm²
The are of the figure is 67.5 cm².
