Questions: PQRS es un rectángulo de largo 6 cm y de ancho 5 cm, ¿Cuál es el área del cuadrilátero ABCD? A) 6 B) 7 C) 8 D) 9 E) Otra especifique: Al rectángulo ABCD se le han inscrito dos circunferencias, ¿Cuál es el perímetro de la figura sombreada?

Solution Steps

The first problem involves finding the area of a trapezoid. The formula for the area of a trapezoid is: \[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \] where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides, and \( h \) is the height.

For the given trapezoid:

• \( b_1 = 6 \) cm
• \( b_2 = 10 \) cm
• \( h = 5 \) cm

\[ \text{Area} = \frac{1}{2} \times (6 + 10) \times 5 = \frac{1}{2} \times 16 \times 5 = 40 \text{ cm}^2 \]

The second problem involves finding the area of a rectangle PQRS with a length of 6 cm and a width of 5 cm. The formula for the area of a rectangle is: \[ \text{Area} = \text{length} \times \text{width} \]

For the given rectangle:

• Length = 6 cm
• Width = 5 cm

\[ \text{Area} = 6 \times 5 = 30 \text{ cm}^2 \]

The third problem involves finding the area of the quadrilateral ABCD, which is a parallelogram. The formula for the area of a parallelogram is: \[ \text{Area} = \text{base} \times \text{height} \]

For the given parallelogram:

• Base = 6 cm
• Height = 2 cm

\[ \text{Area} = 6 \times 2 = 12 \text{ cm}^2 \]

Final Answer