All area formulas are on the SAT reference sheet, but knowing them saves time. Tap any formula to see a diagram and worked example.
l = 8, w = 5
A = 8 × 5 = 40
> } />b = 10, h = 6
A = ½ × 10 × 6 ={" "} 30
> } />b = 9, h = 4
A = 9 × 4 = 36
> } />b₁ = 6, b₂ = 10, h = 4
A = ½(6+10) × 4 ={" "} 32
> } />r = 5
A = π(25) ={" "} 25π ≈ 78.5
> } />d = 10 (r = 5)
C = 2π(5) ={" "} 10π ≈ 31.4
> } />The height of a triangle is ALWAYS perpendicular to the base — it's NOT the side length (unless it's a right triangle).
Break complex shapes into simpler pieces. Add areas for combined shapes. Subtract for cut-out regions.
10 × 8 rectangle with a 4 × 3 piece cut out
80 − 12 ={" "} 68 square units
Square with side 10 and inscribed circle (r = 5)
Shaded area = 100 − 25π ≈{" "} 21.5 square units
A sector is a "pizza slice" of a circle. The fraction of the circle used = central angle ÷ 360°.
Circle with r = 6, central angle = 60°
Arc = (60 ÷ 360) × 2π(6) =
Sector = (60 ÷ 360) × π(36) ={" "} 6π
Surface area is the total area of all faces or surfaces of a 3D shape. Tap any formula to see the shape and a worked example.
l = 4, w = 3, h = 2
SA = 2(12 + 8 + 6)
SA = 2(26) ={" "} 52
> } />r = 3, h = 5
SA = 2π(9) + 2π(15)
SA = 18π + 30π ={" "} 48π ≈ 150.8
> } />r = 4
SA = 4π(16) ={" "} 64π ≈ 201.1
> } />Volume formulas are provided on the SAT reference sheet.{" "} Tap any formula to explore.
l = 6, w = 3, h = 4
V = 6 × 3 × 4 ={" "} 72
> } />r = 5, h = 8
V = π(25)(8) ={" "} 200π ≈ 628.3
> } />r = 4, h = 9
V = ⅓ × π(16)(9)
V ={" "} 48π ≈ 150.8
> } />r = 6
V = ⁴⁄₃ × π(216)
V ={" "} 288π ≈ 904.8
> } />B = 25 (5×5 base), h = 12
V = ⅓ × 25 × 12 ={" "} 100
> } />
A cone is