Question

Find the volume of the pyramid​

Answer 1

1874.6 yd³

Explanation:

The height of the pyramid can be found from the two longer edges using the Pythagorean theorem:

h² = (34 yd)² -(30 yd)² = 256 yd²

h = 16 yd

__

The area of the isosceles triangle base can be found several ways. One of them is using Heron's formula:

B = √(s(s-a)(s-b)(s-c)) where s=(a+b+c)/2 is the semiperimeter

We have sides a=b=30 and c=26, so ...

s = (30+30+26)/2 = 86/2 = 43

B = √(43(43-30)(43-30)(43-26) = 13√(43·17) ≈ 351.481 . . . . yd² base area

__

Then the volume is found from ...

V = (1/3)Bh = (1/3)(351.481 yd²)(16 yd) ≈ 1874.6 yd³

Answer 2

Answer:

Explanation:

The formula for determining the volume of a triangular pyramid is

Volume = 1/3AH

Where

A is the area of the triangular base

H is the height of the pyramid which is the distance from the base to the apex

The perpendicular height of the triangular base of the pyramid is 30 yards. The base of the triangle is 26 yards. Area of the triangular base is expressed as

1/2 × b × h = 1/2 × 26×30 = 390 yard^2

Volume of pyramid = 1/3× 390 × 34

= 13260/3 = 4420 yards ^3