Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
(1 point)
To find the surface area of the rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.
First, calculate the area of the base:
Area of the base = length * width
Area of the base = 14cm * 12cm
Area of the base = 168 square cm
Next, calculate the combined area of the four triangular faces:
Area of each triangular face = (1/2) * base * height
Area of each triangular face = (1/2) * 14cm * 10cm
Area of each triangular face = 70 square cm
Since there are four triangular faces, the combined area of all four faces is:
Combined area of the four faces = 4 * 70 square cm
Combined area of the four faces = 280 square cm
Finally, calculate the total surface area of the rectangular pyramid:
Total surface area = area of the base + combined area of the four faces
Total surface area = 168 square cm + 280 square cm
Total surface area = 448 square cm
Therefore, the surface area of the rectangular pyramid is 448 square cm.