Final answer:
To find the total area of the composite figure described, calculate the area of the trapezoid and the triangle separately and then add them together.
The area of the trapezoid is found using the formula: area = 1/2 * (base1 + base2) * height. The area of the triangle is found using the formula: area = 1/2 * base * height. After calculating the areas, add them together to find the total area of the figure.
Step-by-step explanation:
The figure described in the question is composed of a trapezoid and a triangle. To find the area of the trapezoid, we can use the formula: area = 1/2 * (base1 + base2) * height. In this case, the shorter base is 18 cm, the longer base is unknown, and the height is 12 cm.
To find the longer base, we subtract the portion from the vertex to the perpendicular height (4 cm) from the shorter base: base2 = 18 cm - 4 cm = 14 cm. Plugging these values into the formula, we get: area of trapezoid = 1/2 * (18 cm + 14 cm) * 12 cm = 1/2 * 32 cm * 12 cm = 192 cm^2.
To find the area of the triangle, we can use the formula: area = 1/2 * base * height. In this case, the base is the longer base of the trapezoid (14 cm) and the height is the portion from a point to a vertical line created by two vertices (3 cm).
Plugging these values into the formula, we get: area of triangle = 1/2 * 14 cm * 3 cm = 21 cm^2.
To find the total area of the figure, we add the area of the trapezoid and the area of the triangle: total area = area of trapezoid + area of triangle = 192 cm^2 + 21 cm^2 = 213 cm^2.