Math by First Principles
Level 2 · Intermediate ← Back to lesson

Areas of Quadrilaterals: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered
Question 1 of 12
  1. 1

    A convex trapezoid has area 132132 square cm, perpendicular height 88 cm, and one parallel base 1212 cm. Find the other base.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 12 cm and b. A dashed perpendicular between them is labeled 8 cm, with a right-angle square. 12 cmb8 cmNot to scale
  2. 2

    A rhombus has area 105105 square cm and one full diagonal 1414 cm. Find the other full diagonal.

    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 14 cm. AC is labeled d. A single tick on every side marks all four sides congruent.ABCDO14 cmdNot to scale
  3. 3

    In convex kite ABCDABCD, the equal-side pairs meet at AA and CC. Diagonals meet at OO. Given AOAO is 33 cm, OCOC is 88 cm, and BOBO is 66 cm, find the kite 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. AO is 3 cm. OC is 8 cm. Single side ticks pair AB with AD; double ticks pair BC with CD.ABCDO3 cm8 cmNot to scale
  4. 4

    A convex quadrilateral has a diagonal 1818 cm long. The perpendicular distances of the other vertices from its line are 22 cm and 77 cm. Find its area.

    One diagonal gives two trianglesSchematic convex quadrilateral ABCD, not to scale. AC is a horizontal diagonal labeled 18 cm. Vertex B lies above AC and vertex D below it. Dashed perpendicular heights from B and D to AC are labeled 2 cm and 7 cm. Right-angle squares mark their feet. BD is not drawn or asserted perpendicular to AC.ABCD18 cm2 cm7 cmNot to scale
  5. 5

    A convex trapezoid has parallel bases 3x3x cm and (x+4)(x+4) cm and perpendicular height 55 cm. Its area is 7070 square cm. Find xx.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 3x cm and (x+4) cm. A dashed perpendicular between them is labeled 5 cm, with a right-angle square. 3x cm(x+4) cm5 cmNot to scale
  6. 6

    A convex quadrilateral has diagonals 88 cm and 1313 cm. No angles or quadrilateral family are given. What follows about its area?

  7. 7

    A trapezoidal tile has parallel bases 1717 cm and 99 cm and perpendicular height 66 cm. A rectangular tile has dimensions 1212 cm by 66 cm. How much greater is the trapezoid area?

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 9 cm and 17 cm. A dashed perpendicular between them is labeled 6 cm, with a right-angle square. 9 cm17 cm6 cmNot to scale
  8. 8

    A square has a full diagonal of 1212 cm. Find its area.

    A square and its given diagonalA square with one full diagonal labeled 12 cm. Right-angle marks identify the corners.12 cm
  9. 9

    A convex trapezoid has bases 77 cm and 1919 cm and perpendicular height 1212 cm. Its midsegment is 1313 cm. Which area computation is justified?

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 7 cm and 19 cm. A dashed perpendicular between them is labeled 12 cm, with a right-angle square. 7 cm19 cm12 cmNot to scale
  10. 10

    A convex kite has full diagonals 9.69.6 cm and 7.57.5 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 9.6 cm. AC is labeled 7.5 cm. Single side ticks pair AB with AD; double ticks pair BC with CD.ABCDO9.6 cm7.5 cmNot to scale
  11. 11

    A convex quadrilateral has perpendicular diagonals meeting at OO. One diagonal is 2020 cm long. The other is split at OO into 44 cm and 99 cm. Find its area.

    Perpendicular diagonals partition the areaSchematic convex quadrilateral 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 20 cm. AO is 4 cm. OC is 9 cm. No side equality or diagonal bisection is asserted.ABCDO20 cm4 cm9 cmNot to scale
  12. 12

    A convex trapezoid has area 58.558.5 square cm and parallel bases 88 cm and 1818 cm. Find its perpendicular height.

    Parallel bases and perpendicular heightSchematic trapezoid, not to scale. Parallel top and bottom bases are labeled 8 cm and 18 cm. A dashed perpendicular between them is labeled h, with a right-angle square. 8 cm18 cmhNot to scale
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