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Rectangle under a parabola

Rectangle under a parabola
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2015-02-13 23:26
Coordinate Geometry
This example demonstrates the geometric figure of a rectangle located below a parabola. The key mathematical concepts include the parabola equation, rectangle area calculation, and geometric relationships in coordinate geometry. Construction involves GeoGebra commands such as Intersect, Segment, Polygon, and area calculations. Suitable for high school students or college freshmen learning analytic geometry and area computation.

GeoGebra Commands & Parameters

  1. Intersect(f, a, (0.75, 3.4375)) → B
  2. Segment(C, B) → b
  3. Segment(B, A) → c
  4. Segment(A, D) → d
  5. Segment(D, C) → e
  6. LaTeX(AREA, true, true) → AREA_1
  7. Polygon(C, B, A, D) → poly1, c_1, b_1, a_1, d_1
  8. LaTeX(AREA, true, true) → text1
  9. AttachCopyToView(PolyLine[(1.2702033364061383, 3.032105433015351), (1.2976093029177909, 3.0869173660386564), (1.3524212359410963, 3.1417292990619616), (1.4072331689644018, 3.182838248829441), (1.4620451019877072, 3.2102442153410933), (1.530560018266839, 3.2650561483643985), (1.571668968034318, 3.2924621148760513), (1.6264809010576236, 3.3061650981318778), (1.6675898508251028, 3.3198680813877037), (1.7086988005925818, 3.33357106464353), (1.7498077503600609, 3.360977031155183), (1.7909167001275401, 3.3883829976668354), (1.8320256498950191, 3.415788964178488), (1.8731345996624982, 3.429491947434314), (1.9142435494299774, 3.4431949306901406), (1.9690554824532829, 3.4431949306901406), (2.0375703987324147, 3.4706008972017934), (2.0786793484998936, 3.4843038804576194), (2.1334912815231992, 3.4843038804576194), (2.1883032145465044, 3.4843038804576194), (2.24311514756981, 3.4843038804576194), (2.2979270805931153, 3.4843038804576194), (2.3664419968722474, 3.4843038804576194), (2.4075509466397267, 3.5117098469692722), (NaN, NaN), (1.3250152694294437, 3.2650561483643985), (1.3250152694294437, 3.2102442153410933), (1.3250152694294437, 3.155432282317788), (1.3113122861736173, 3.100620349294483), (1.3524212359410963, 3.1143233325503092), (1.4072331689644018, 3.1143233325503092), (1.4620451019877072, 3.1143233325503092), true], 1, (-6.362358337089147, -2.298355053501084), (8.35464567966837, 6.15638561534375), (-126, 575), (948, -42.00000000000001)) → stroke1

AI Drawing Prompt Reference

Draw a parabola with a rectangle below it. The rectangle should touch the parabola at one side and have one side parallel to the x-axis. Calculate and display the area of the rectangle, showing the geometric relationship between the parabola and the rectangle. Connect the intersection points of the parabola with the x-axis to the rectangle's vertices, forming the rectangle, and finally connect the vertices with a smooth curve to complete the shape.
The prompt above was compiled from the original drawing commands and is for reference only.