Image Description

The image is a multiple-choice math problem presented on a light gray background. It focuses on calculating the area of a composite shape made up of two trapezoids.

Problem Setup:

Shape: Two trapezoids are joined together. The image provides a diagram of the shape with labeled side lengths in centimeters.
Measurements: The diagram shows the following measurements:
Top trapezoid: Bases of 8 cm and 6 cm, height of 5 cm.
Bottom trapezoid: Bases of 6 cm and 9 cm, height of 5 cm.
Question: "What is the area of the figure in square ceintimeters?" (Note: "ceintimeters" is likely a typo and should be "centimeters").
Multiple Choice Answers:

Four answer options are provided:

35 cm²
72.5 cm² (This option is highlighted, indicating it's the selected answer)
33 cm²
78.25 cm²

1 answer

To find the area of the composite shape made up of the two trapezoids, we'll calculate the area of each trapezoid separately using the formula for the area of a trapezoid:

\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]

where \(b_1\) and \(b_2\) are the lengths of the two bases, and \(h\) is the height.

Top Trapezoid:

  • Bases: \(b_1 = 8\) cm and \(b_2 = 6\) cm
  • Height: \(h = 5\) cm

Calculating the area:

\[ \text{Area}_{\text{top}} = \frac{1}{2} \times (8 + 6) \times 5 \] \[ = \frac{1}{2} \times 14 \times 5 \] \[ = 7 \times 5 = 35 \text{ cm}^2 \]

Bottom Trapezoid:

  • Bases: \(b_1 = 6\) cm and \(b_2 = 9\) cm
  • Height: \(h = 5\) cm

Calculating the area:

\[ \text{Area}_{\text{bottom}} = \frac{1}{2} \times (6 + 9) \times 5 \] \[ = \frac{1}{2} \times 15 \times 5 \] \[ = 7.5 \times 5 = 37.5 \text{ cm}^2 \]

Total Area: Now, we add the areas of both trapezoids:

\[ \text{Total Area} = \text{Area}{\text{top}} + \text{Area}{\text{bottom}} \] \[ = 35 + 37.5 = 72.5 \text{ cm}^2 \]

Thus, the total area of the figure is \(72.5 \text{ cm}^2\).

The highlighted answer option \(72.5 \text{ cm}^2\) is correct.