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2 years ago

Find the surface area of the square pyramid shown below. (Measurements in picture)

Mathematics

2 answers:

Sloan [31]2 years ago

8 0

Given:

Side length of base = 8

Slant height = 6

To find:

The surface area of the square pyramid.

Solution:

Surface area:

$$SA=A+\frac{1}{2} p s$

where A is the area of base

p is the perimeter of base

s is the slant height

Area of base (A) = 8 × 8

= 64

Perimeter of base(P) = 4 × 8

= 32

Substitute these in the formula:

$$SA=64+\frac{1}{2} \times 32 \times 6$

$$SA=64+96$

$$SA=160$

The surface area of the square pyramid is 160 unit².

miskamm [114]2 years ago

6 0

Answer:

160

Step-by-step explanation:

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2 years ago

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .