Quadrilaterals — Practice Quiz

A Geometry cheat sheet for Quadrilaterals — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Square

$$A = s^2, \quad P = 4s, \quad d = s\sqrt{2}$$

Where: \(s\) = side, \(d\) = diagonal

Rectangle

$$A = lw, \quad P = 2(l+w), \quad d = \sqrt{l^2 + w^2}$$

Where: \(l\) = length, \(w\) = width

Parallelogram Area

$$A = bh = ab\sin\theta$$

Where: \(b\) = base, \(h\) = height, \(\theta\) = angle

Rhombus Area

$$A = \frac{1}{2}d_1 d_2$$

Where: \(d_1, d_2\) = diagonals

Trapezoid Area

$$A = \frac{1}{2}(b_1 + b_2)h$$

Where: \(b_1, b_2\) = bases, \(h\) = height

Kite Area (alternate form)

$$A = \frac{1}{2}d_1 d_2 \sin\theta$$

Where: \(\theta\) = angle between diagonals

Cyclic Quadrilateral (Brahmagupta)

$$A = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$

Where: \(s\) = semi-perimeter

Practice quiz

  1. If a square has a diagonal of $10 \text{ cm}$, what is its area?

    • $50 \text{ cm}^2$
    • $100 \text{ cm}^2$
    • $25\sqrt{2} \text{ cm}^2$
    • $20 \text{ cm}^2$

    Answer: $50 \text{ cm}^2$

  2. A rectangle has a length of $8 \text{ m}$ and a width of $6 \text{ m}$. What is the length of its diagonal?

    • $14 \text{ m}$
    • $10 \text{ m}$
    • $20 \text{ m}$
    • $48 \text{ m}$

    Answer: $10 \text{ m}$

  3. The parallel bases of a trapezoid are $7 \text{ cm}$ and $13 \text{ cm}$, and its height is $6 \text{ cm}$. Calculate the area of the trapezoid.

    • $120 \text{ cm}^2$
    • $60 \text{ cm}^2$
    • $30 \text{ cm}^2$
    • $42 \text{ cm}^2$

    Answer: $60 \text{ cm}^2$

  4. A parallelogram has adjacent sides of length $10 \text{ m}$ and $8 \text{ m}$, with an angle of $60^\circ$ between them. What is its area?

    • $80 \text{ m}^2$
    • $40 \text{ m}^2$
    • $40\sqrt{3} \text{ m}^2$
    • $20\sqrt{3} \text{ m}^2$

    Answer: $40\sqrt{3} \text{ m}^2$

  5. The diagonals of a rhombus measure $10 \text{ cm}$ and $24 \text{ cm}$. What is the area of the rhombus?

    • $60 \text{ cm}^2$
    • $120 \text{ cm}^2$
    • $240 \text{ cm}^2$
    • $17 \text{ cm}^2$

    Answer: $120 \text{ cm}^2$

  6. A kite has diagonals of length $8 \text{ cm}$ and $12 \text{ cm}$. If the angle between the diagonals is $30^\circ$, what is its area?

    • $48 \text{ cm}^2$
    • $24 \text{ cm}^2$
    • $12 \text{ cm}^2$
    • $96 \text{ cm}^2$

    Answer: $24 \text{ cm}^2$

  7. A cyclic quadrilateral has sides $a=3, b=4, c=5, d=6$. Using Brahmagupta's formula, calculate its area.

    • $6\sqrt{10}$
    • $18$
    • $36$
    • $12\sqrt{5}$

    Answer: $6\sqrt{10}$

  8. A square has the same perimeter as a rectangle with length $10 \text{ cm}$ and width $6 \text{ cm}$. What is the area of the square?

    • $32 \text{ cm}^2$
    • $64 \text{ cm}^2$
    • $16 \text{ cm}^2$
    • $100 \text{ cm}^2$

    Answer: $64 \text{ cm}^2$

  9. A rhombus has a side length of $5 \text{ cm}$ and one of its diagonals is $6 \text{ cm}$. What is its area?

    • $15 \text{ cm}^2$
    • $24 \text{ cm}^2$
    • $30 \text{ cm}^2$
    • $48 \text{ cm}^2$

    Answer: $24 \text{ cm}^2$

  10. A rectangular garden has an area of $120 \text{ m}^2$ and a length of $15 \text{ m}$. What is the perimeter of the garden?

    • $23 \text{ m}$
    • $46 \text{ m}$
    • $30 \text{ m}$
    • $60 \text{ m}$

    Answer: $46 \text{ m}$

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