Respuesta :
Answer:
The slant height is 5 inches .
Step-by-step explanation:
Given as :
The total surface area of square base pyramid = [tex]T_p[/tex] = 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 × [tex]\dfrac{1}{2}[/tex] × 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, [tex]T_p[/tex] = 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 = [tex]\dfrac{120 }{24}[/tex]
i.e h =5 inches
So, The slant height = h = 5 inches
Hence,The slant height is 5 inches . Answer
