What is the surface area of the figure above? Georgia Milestones Grade 7 Mathematics Formula Sheet (1 point) Responses 78 centimeters squared 78 centimeters squared 92 centimeters squared 92 centimeters squared 84 centimeters squared 84 centimeters squared 66 centimeters squared
5cm 6cm 4cm 3cm
To find the surface area of this figure, we need to calculate the area of each individual face and then add them together.
The figure consists of a rectangular prism with dimensions 5cm (length) x 6cm (width) x 4cm (height) and a pyramid with a base of 5cm x 6cm and a height of 3cm.
Surface area of rectangular prism:
- Top and bottom faces: 5cm * 6cm = 30cm^2 (each)
- Side faces: 5cm * 4cm = 20cm^2 (each) and 6cm * 4cm = 24cm^2 (each)
Total surface area of rectangular prism = 2(30) + 2(20) + 2(24) = 60 + 40 + 48 = 148 cm^2
Surface area of pyramid:
- Base: 5cm * 6cm = 30cm^2
- Side faces (triangular): 1/2 * base * height = 1/2 * 5cm * 3cm = 7.5 cm^2 (each)
Total surface area of pyramid = 30 + 3(7.5) = 30 + 22.5 = 52.5 cm^2
Total surface area of the figure = Surface area of rectangular prism + surface area of pyramid = 148 cm^2 + 52.5 cm^2 = 200.5 cm^2
Therefore, the surface area of the figure above is approximately 200.5 cm^2. None of the given answer choices match this calculation exactly, so the best option would be to round to the nearest whole number, which would be 200.