Asquare pyramid has a total surface area of 264
square inches and the side length of its base is 12
inches. determine the side length of its square base

The slant height is 5 inches .

Step-by-step explanation:

Given as :

The total surface area of square base pyramid = = 264 inches²

The side length of the square base pyramid = b = 12 inches

Let The slant height = h inches

Now, According to question

∵Total surface area of square base pyramid = area of the square base + area of each faces of triangle

So, Area of square base = side × side

i.e Area of square base = b × b

or, Area of square base = 12 inches × 12 inches

∴  Area of square base = 144 inches²

Again

Area of each faces of triangle

Since it has 4 triangle So, Area of 4 faces triangle = 4 × × base × slant height

So, Area of 4 faces triangle = 2 × b ×  h

Or, Area of 4 faces triangle = 2 × 12 inches ×  h

or, Area of 4 faces triangle = 24 inches ×  h

So,Total surface area of square base pyramid = 144 inches² + 24 inches ×  h

or, = 144 inches² + 24 inches ×  h

Or, 264 inches² = 144 inches² + 24 inches ×  h

Or, 264 inches² - 144 inches² = 24 inches ×  h

Or,  120 inches² = 24 inches ×  h

∴  h =

i.e h =5 inches

So, The slant height = h = 5 inches

Hence,The slant height is 5 inches . Answer

squares, rhombus, rectangles