a) Construct a right square pyramid with your choice of dimensions (maximum base of 5 by 5 units).
base dimensions:
Slant height:
Calculate its surface area
To construct a right square pyramid, we need to determine the base dimensions and the slant height first. Then we can calculate its surface area.
Step 1: Choose the base dimensions
In this case, we'll choose a maximum base of 5 by 5 units. For simplicity, let's use a base of 4 by 4 units.
Step 2: Calculate the slant height
The slant height can be found using the Pythagorean Theorem. Since we have a right square pyramid, the slant height is the hypotenuse of a right triangle with the base of the triangle as one side and the height of the pyramid as the other side.
In a right triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume the height of the pyramid is h.
Using the base dimensions, the sides of the triangle are 4 (base) and h (height). We can calculate the slant height (l) as follows:
l^2 = 4^2 + h^2
l^2 = 16 + h^2
l = √(16 + h^2)
Step 3: Calculate the surface area
The surface area of a right square pyramid can be found by summing the areas of the base and the four triangular faces.
The formula for the surface area is:
Surface area = Base area + 4 * (0.5 * Base * Slant height)
First, let's calculate the base area:
Base area = side^2 = 4^2 = 16 square units
Next, calculate the slant height using the height (h) of the pyramid you want.
Finally, use the formula to find the surface area by substituting the calculated values:
Surface area = 16 + 4 * (0.5 * 16 * slant height)
Plug in the calculated slant height and perform the calculations to find the surface area.