Answer:
360 ft^2
Step-by-step explanation:
The surface area of a right square pyramid can be found using the formula: [tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex]
In this formula:
- a = base edge (the length of the sides of the square)
- h = height of the pyramid
In this diagram, the base edge length is 10 ft and the height of the square pyramid is 12 ft. Substitute these values into the formula to find the surface area.
- [tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex]
- [tex](10)^2+2(10)\sqrt{\frac{(10)^2}{4}+(12)^2[/tex]
Simplify this expression. Start by evaluating the exponents then rewrite the expression.
- [tex](100)+2(10)\sqrt{\frac{(100)}{4}+(144)[/tex]
Now evaluate inside the radical sign.
- [tex](100)+2(10)\sqrt{(25)+(144)[/tex]
- [tex](100)+2(10)\sqrt{169[/tex]
Multiply 2 and 10 together (we're following the rules of PEMDAS).
- [tex](100)+(20)\sqrt{169[/tex]
Find the square root of 169 then multiply that by 20.
- [tex](100)+(20)(13)[/tex]
- [tex](100)+(260)[/tex]
Finish the problem by adding 100 and 260 together.
The surface area of the pyramid is [tex]\boxed{\text {360 ft}^2}[/tex].
