Answer: 616 cm²
Step-by-step explanation: In this problem, we are asked to find the surface area of the given pyramid.
To find the surface area of a pyramid, we simply add the areas of the faces of the pyramid. Let's first start with the base for the given pyramid.
We can see that the base is a square with sides that each have a length of 14 centimeters. Remember that the formula for the area of a square is S².
So, the formula for the area of the base of the pyramid is S². Since each side has a length of 14 centimeters, we have (14 cm)² which equals 196 cm².
This means that the area of the base of the pyramid is 196 cm².
Next, notice that there are four sides of the pyramid and each side is a triangle with a base of 14 centimeters and a height of 15 centimeters. Remember that the formula for the area of a triangle is 1/2 base × height. This means that the formula for the area of each side of the pyramid is 1/2 bh.
Since each side has a base of 14 centimeters and a height of 15 centimeters, we can plug this information into the formula to get 1/2 (14 cm) (15 cm). 14 centimeters x 15 centimeters is 210 centimeters² and 1/2 × 210 cm² is 105 cm².
This means that the area of each side of the pyramid is 105 cm².
Therefore, the area of all four sides of the pyramid is 4 × 105 cm² which equals 420 cm².
Finally, to find the total surface area of the given pyramid we must add the area of the base which is 196 cm² and add the area of all four sides of the pyramid which is 420 cm².
196 cm² + 420 cm² = 616 cm².
This means that the total surface area of the given pyramid is 616 cm².