Question

the model of a pyramid has a square base. each side of the base measures 3 1/2 feet. The slant height of each triangular face measures 7 feet. What is the approximate surface area of the pyramid?

Answer 1

My assumption is that your "slant height" is the distance from the bottom of the pyramid to the top on one of the edges. That being said, you have 4 isoceles triangles each with a base of 3.5 feet, and other side lengths of 7 feet. to find the height, you need to use either pythagorean theorem or trigonometry.
Using pythagorean: draw a height line that is perpendicular to the base side on one triangle that runs through the vertex opposite the base side. This is your height. You now have two of the three sides of a right triangle where \[7^2=1.75^2+x^2\] notice that you use 1.75, because it is half of your base side for the triangle.
This height is approx. 6.78. at this point you sum the four triangle areas and the square base area of 3.5 squared.
A=4(\[1/2 bh+3.5^2\]