Mrs.D Math · 7th Grade

VOLUME
QUEST

Volume of Triangular Pyramids
½Bh = V
B = b × h‑tri
units³
🔍 Find Volume
🔢 Missing Height
🎲 Mixed
🔍 Find Volume
🔢 Missing Height
🎲 Mixed
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📚 Volume of Triangular Pyramids

The Formula

½Bh = V

where B = b × htri (triangle base × triangle height) and h = pyramid height — then multiply by ⅓ for the pyramid

Full formula: V = ⅓ × ½ × b × htri × H = ⅓ × B × H

1
Find B — multiply the triangle base (b) by the triangle height (h), then multiply by ½.
b=8, h=5 → B = ½ × 8 × 5 = 20
2
Multiply B × H × ⅓ — B is the triangular base area, H is the pyramid height, and ⅓ is for the pyramid shape.
B=20, H=9 → V = ⅓ × 20 × 9 = 60 units³

Example 1 — Find Volume

8 ft 5 ft 9 ft

b=8 ft,  h=5 ft,  H=9 ft

B = ½ × 8 × 5 = 20
V = ⅓ × 20 × 9
V = ⅓ × 180
V = 60 ft³

Example 2 — Find Pyramid Height (H)

8 ft 5 ft ? ft

V=60 ft³,  b=8 ft,  h=5 ft

B = ½ × 8 × 5 = 20
⅓ × 20 × H = 60
20H ÷ 3 = 60
20H = 180
H = 180 ÷ 20
H = 9 ft

⚠ Remember

!
b and h are the triangle's dimensions — they form a right angle. h is perpendicular to b.
!
H is the pyramid height — the perpendicular distance from the base to the apex. Don't confuse it with h!
!
Don't forget × ⅓! — Pyramids are one-third the volume of a prism with the same base and height.
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FIND VOLUME
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