Question

What is the surface area of a square pyramid with a base side lengths of 10 inches and a slant height of 14 inches

Answer 1

You could find the surface area using two different methods, but coming out with the same answer.

Method One: This method involves using an equation that helps finding the surface area for a square pyramid.

The equation: A+(1/2)ps=SA; we should break down what the letters stand for. A=Area of the base; the area of the base is 10×10=100 P= perimeter of the base; 10×4=40 S= Slant height;14

Let's put these values into the equation and find the surface area. 100+(1/2)(40)(14)=100+(20)(14)=100+280=380 The surface area is 380 in².

Method Two: The picture below shows how to lay out the square pyramid so you can find the area of each the shapes, then add them up. There are four triangles and a square.

Triangles: We use the equation (1/2)BH; let's plug the values in. 1/2(10)(14)=1/2(140)=70; there are four triangles, so let's multiply by four to find the area of all four of them triangles together. 70×4=280

Square: It's the side length squared. 10²=100; let's add everything together.

The four triangles+the square= the surface area

280+100=380

So, the surface area is 380 in².

Answer 2

Well I’m not gonna right as much as the first person did but the answer is in fact 380in because if u multiply height(14) and width(10)(in this case sense the length and height are the same it’s ok to skip a step) it would give you 140 but because a triangle isn’t a full square and is only half a square u have to divide it by 2 and that would give you 70 so 70 times 4 because there are 4 of the same faces you will get 280. Now you have to find the base which is length times width and that would give you 100 finally you would add up all the these two numbers which will leave you with 380. :)