Answer:
67.5 cm²
Step-by-step explanation:
The figure can be decomposed into figures whose area formulas you know.
<h3>Decomposition</h3>
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.
<h3>Trapezoid</h3>
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
<h3>Rectangle</h3>
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
<h3>Total area</h3>
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.