Observe the figure:

Length of the base of the pyramid is .

Slant height of the pyramid is .

(a)

Total surface area of the pyramid is .

Therefore, .

Substitue corresponding values in  the formula.

.

Total surface area of the pyramid is  sq-cm.

(b)

Length of the base of the pyramid is .

Altitude of the pyramid is .

Find the volume of the pyramid.

Volume of the square pyramid .

Where is the area of the base.

Area of the square base is .

Substitue corresponding values in  the formula.

Volume of the pyramid is cubic-cm.

edited Feb 10, 2016 by cameron

(4)

Step 1:

(a)

Observe the figure:

Inscribed angle theorem of circle:

If the inscribed angle measure x, the central angle will measure 2x.

.

The triangle DAB is right angled triangle and DB is the hypotenuse.

Therefore, .

Step 2:

(b)

Find .

Draw an angle bisector from A.

Angle .

Therefore, .

Redraw the figure:

From the triangle ACB: .

Therefore, .

Step 3:

(c)

Find .

From the triangle ACD: .

Therefore .

Step 4:

(d)

From triangle ABD: .

Therefore,

Solution:

(a) .

(b) .

(c) .

(d)