import React, { useState } from "react"; import { Square, Circle, Box, Layers, Ruler, BookOpen, ChevronDown, } from "lucide-react"; import LessonShell, { ConceptCard, FormulaBox, ExampleCard, TipCard, PracticeFromDataset, } from "../../../components/lessons/LessonShell"; import { Frac } from "../../../components/Math"; import CompositeAreaWidget from "../../../components/lessons/CompositeAreaWidget"; import InteractiveSectorWidget from "../../../components/lessons/InteractiveSectorWidget"; import CompositeSolidsWidget from "../../../components/lessons/CompositeSolidsWidget"; import ScaleFactorWidget from "../../../components/lessons/ScaleFactorWidget"; import { AREA_VOL_EASY, AREA_VOL_MEDIUM } from "../../../data/math/area-volume"; /* ─── Clickable formula card with shape diagram + example ─── */ function FormulaCard({ formula, diagram, example, }: { formula: React.ReactNode; diagram: React.ReactNode; example: React.ReactNode; }) { const [open, setOpen] = useState(false); return ( ); } /* ─── Shape SVG diagrams ─── */ const RectSvg = () => ( l = 8 w = 5 ); const TriSvg = () => ( b = 10 h = 6 ); const ParaSvg = () => ( b = 9 h = 4 ); const TrapSvg = () => ( b₁ = 6 b₂ = 10 h = 4 ); const CircAreaSvg = () => ( r = 5 ); const CircCircSvg = () => ( d = 10 ); const PrismSASvg = () => ( l = 4 h = 2 w = 3 ); const CylSASvg = () => ( r = 3 h = 5 ); const SphereSvg = () => ( r = 4 ); const PrismVolSvg = () => ( l = 6 h = 4 w = 3 ); const CylVolSvg = () => ( r = 5 h = 8 ); const ConeSvg = () => ( h = 9 r = 4 ); const SphereVolSvg = () => ( r = 6 ); const PyramidSvg = () => ( h = 12 B = 25 ); interface LessonProps { onFinish?: () => void; } const SECTIONS = [ { title: "Area Formulas", icon: Square }, { title: "Composite Shapes", icon: Layers }, { title: "Arc Length & Sector Area", icon: Circle }, { title: "Surface Area", icon: Box }, { title: "Volume", icon: Ruler }, { title: "Practice & Quiz", icon: BookOpen }, ]; export default function AreaVolumeLesson({ onFinish }: LessonProps) { return ( {/* Section 1: Area Formulas */}

Area Formulas

All area formulas are on the SAT reference sheet, but knowing them saves time. Tap any formula to see a diagram and worked example.

} example={ <>

l = 8, w = 5

A = 8 × 5 = 40

} /> Triangle: A = × b × h } diagram={} example={ <>

b = 10, h = 6

A = ½ × 10 × 6 ={" "} 30

} /> } example={ <>

b = 9, h = 4

A = 9 × 4 = 36

} /> Trapezoid: A = (b₁ + b₂) × h } diagram={} example={ <>

b₁ = 6, b₂ = 10, h = 4

A = ½(6+10) × 4 ={" "} 32

} /> } example={ <>

r = 5

A = π(25) ={" "} 25π ≈ 78.5

} /> } example={ <>

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).

{/* Section 2: Composite Shapes */}

Composite Shapes

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

{/* Section 3: Arc Length & Sector Area */}

Arc Length & Sector Area

A sector is a "pizza slice" of a circle. The fraction of the circle used = central angle ÷ 360°.

Arc Length = (θ ÷ 360) × 2πr Sector Area = (θ ÷ 360) × πr²

Circle with r = 6, central angle = 60°

Arc = (60 ÷ 360) × 2π(6) = × 12π = 2π

Sector = (60 ÷ 360) × π(36) ={" "}

{/* Section 4: Surface Area */}

Surface Area

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.

} example={ <>

l = 4, w = 3, h = 2

SA = 2(12 + 8 + 6)

SA = 2(26) ={" "} 52

} /> } example={ <>

r = 3, h = 5

SA = 2π(9) + 2π(15)

SA = 18π + 30π ={" "} 48π ≈ 150.8

} /> } example={ <>

r = 4

SA = 4π(16) ={" "} 64π ≈ 201.1

} />
{/* Section 5: Volume */}

Volume

Volume formulas are provided on the SAT reference sheet.{" "} Tap any formula to explore.

} example={ <>

l = 6, w = 3, h = 4

V = 6 × 3 × 4 ={" "} 72

} /> } example={ <>

r = 5, h = 8

V = π(25)(8) ={" "} 200π ≈ 628.3

} /> Cone: V = πr²h } diagram={} example={ <>

r = 4, h = 9

V = ⅓ × π(16)(9)

V ={" "} 48π ≈ 150.8

} /> Sphere: V = πr³ } diagram={} example={ <>

r = 6

V = ⁴⁄₃ × π(216)

V ={" "} 288π ≈ 904.8

} /> Pyramid: V = Bh } diagram={} example={ <>

B = 25 (5×5 base), h = 12

V = ⅓ × 25 × 12 ={" "} 100

} />

A cone is of a cylinder with the same base and height. A pyramid is of a prism with the same base and height.

{/* Section 6: Practice */}

Practice

{AREA_VOL_EASY.slice(0, 2).map((q) => ( ))} {AREA_VOL_MEDIUM.slice(0, 1).map((q) => ( ))}
); }