Math by First Principles
Level 1 · Foundational ← Back to lesson

Areas of Quadrilaterals: Practice

12 multiple-choice questions, progressively harder.

Level 1 · Foundational 0 / 12 answered
Question 1 of 12
  1. 1

    A convex trapezoid has parallel bases 66 cm and 1515 cm and perpendicular height 88 cm. Find its area.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 6 cm and 15 cm. A dashed perpendicular between them is labeled 8 cm, with a right-angle square. 6 cm15 cm8 cmNot to scale
  2. 2

    In a convex trapezoid the parallel bases are 1010 cm and 1616 cm. Its perpendicular height is 99 cm and one slanted leg is 1212 cm. Find its area.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 10 cm and 16 cm. A dashed perpendicular between them is labeled 9 cm, with a right-angle square. The right slanted side is labeled 12 cm.10 cm16 cm9 cm12 cmNot to scale
  3. 3

    A parallelogram has base 1111 cm and corresponding perpendicular height 77 cm. Treat it as an inclusive trapezoid. What area results?

  4. 4

    A rhombus has full diagonals 99 cm and 1616 cm. Find its area.

    Perpendicular diagonals partition the areaSchematic rhombus ABCD, not to scale. A is above O, B right, C below, D left. Diagonals AC and BD intersect at O with a right-angle square. BD is labeled 9 cm. AC is labeled 16 cm. A single tick on every side marks all four sides congruent.ABCDO9 cm16 cmNot to scale
  5. 5

    A convex kite has full diagonals 77 cm and 1818 cm. Find its area.

    Perpendicular diagonals partition the areaSchematic convex kite ABCD, not to scale. A is above O, B right, C below, D left. Diagonals AC and BD intersect at O with a right-angle square. BD is labeled 7 cm. AC is labeled 18 cm. Single side ticks pair AB with AD; double ticks pair BC with CD.ABCDO7 cm18 cmNot to scale
  6. 6

    Which information is enough to use A=12d1d2A=\tfrac12d_1d_2 for a convex quadrilateral?

  7. 7

    Two congruent copies of a trapezoid with bases 88 cm and 1313 cm and height 44 cm join along a leg to form a parallelogram. What is the area of the joined parallelogram?

    Two congruent trapezoids make a parallelogramSchematic joined arrangement, not to scale. Two congruent convex trapezoids, each with parallel bases 13 cm and 8 cm and perpendicular height 4 cm, meet along a leg after a half turn. The original has a solid blue outline; the turned copy has a dashed red outline. The outside is a parallelogram. On each outside base the lengths 13 cm and 8 cm lie end to end. A dashed perpendicular height 4 cm has a right-angle mark.8131384OriginalTurned copyNot to scale
  8. 8

    A convex trapezoid has area 108108 square cm and parallel bases 1212 cm and 2424 cm. Find its perpendicular height.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 12 cm and 24 cm. A dashed perpendicular between them is labeled h, with a right-angle square. 12 cm24 cmhNot to scale
  9. 9

    A convex kite has area 9090 square cm and one full diagonal of 1515 cm. Find its other full diagonal.

    Perpendicular diagonals partition the areaSchematic convex kite ABCD, not to scale. A is above O, B right, C below, D left. Diagonals AC and BD intersect at O with a right-angle square. BD is labeled 15 cm. AC is labeled d. Single side ticks pair AB with AD; double ticks pair BC with CD.ABCDO15 cmdNot to scale
  10. 10

    A diagonal of a convex quadrilateral is 1414 cm. The perpendicular distances from the other vertices to its line are 55 cm and 33 cm. Find the area.

    One diagonal gives two trianglesSchematic convex quadrilateral ABCD, not to scale. AC is a horizontal diagonal labeled 14 cm. Vertex B lies above AC and vertex D below it. Dashed perpendicular heights from B and D to AC are labeled 5 cm and 3 cm. Right-angle squares mark their feet. BD is not drawn or asserted perpendicular to AC.ABCD14 cm5 cm3 cmNot to scale
  11. 11

    Which listed quadrilateral must satisfy the perpendicular-diagonal area formula?

  12. 12

    A convex trapezoid has parallel bases 4.54.5 cm and 9.59.5 cm, with perpendicular height 55 cm. Find its area.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 4.5 cm and 9.5 cm. A dashed perpendicular between them is labeled 5 cm, with a right-angle square. 4.5 cm9.5 cm5 cmNot to scale
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