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

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.

38.5

step-by-step explanation:

lets say, first number = r

second number = 3r+7

total = 49

(r)+(3r+7)= 49

4r+7 = 49

4r = 42

r = 42/4

r= 10.5

3r+7 = 3(10.5)+7 = 38.5

hope this