A square-based pyramid has a surface area of 561 cm². If the length of the base is 11 cm, find the height of the triangular faces.

Step-by-step explanation:

The formula for the area of a square is:

A

=

s

2

Where:

A

is the area of the square.

s

is the length of the side of a square.

Substituting and solving for

s

gives:

225

cm

2

=

s

2

We can take the square root of each side of the equation giving:

√

225

cm

2

=

√

s

2

15

cm

=

s

s

=

15

cm

The formula for the perimeter of a square is:

p

=

4

s

Where:

p

is the perimeter of the square.

s

is the length of the side of a square.

Substituting for

s

from the solution for the previous formula and calculating

p

gives:

p

=

4

×

15

cm

p=60cm

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47 - 90 = 43

43 - 180 = x

x = 137