Answer:
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
<u>Now, According to question</u>
∵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
<u>Area of each faces of triangle</u>
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