Question

PLEASE I REALLY NEED HELP, MY MATH CLASS IS DUE TOMORROW!!!!! ASAP!!!!!!

Answer 1

13.3 ft

Explanation:

`\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}`
`\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=(1)/(2)bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

The surface area of a square-based pyramid is made up of:

• 1 square (the base)
• 4 congruent triangles (the sides)

Given:

• Total SA = 158 feet²
• s = 5 feet
• h = l feet

Find the area of the square base and the area of one of the triangles by substituting the given values into the formulas:

`\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2`

`\textsf{Area of one of the side triangles} = (1)/(2) \cdot 5 \cdot l= 2.5l \; \sf ft^2`

Substitute these values along with the given total surface area into the formula and solve for l:

`\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=(133)/(10)\\l&=13.3\; \sf ft\end{aligned}`

Therefore, the missing length is 13.3 feet.