GED Math Quiz: Geometry 2d

What this quiz covers

This quiz focuses on Geometry 2d, giving you a quick way to practice the rules, question types, and explanations that matter most for GED Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $1,049.44
2. $1,134.72
3. $1,188.00
4. $1,048.72 (correct answer)

Explanation: Garden area = $24 \times 18 = 432$ sq ft. Fountain radius = 4 ft, so fountain area = $\pi(4)^2 = 50.24$ sq ft. Sod area = $432 - 50.24 = 381.76$ sq ft. Cost = $381.76 \times 2.75 = \$1,048.72$. A uses radius 4 but subtracts wrongly. B uses diameter as radius. C ignores the fountain.

Question 2

1. $320 \text{ ft}^2$ (correct answer)
2. $416 \text{ ft}^2$
3. $512 \text{ ft}^2$
4. $304 \text{ ft}^2$

Explanation: Trapezoid area = $\frac{1}{2}(22+30)(16) = \frac{1}{2}(52)(16) = 416$ ft². Pool area = $8 \times 12 = 96$ ft². Deck area = 416 − 96 = 320 ft². B is trapezoid without subtracting pool. C adds the pool. D uses wrong base sum.

Question 3

1. $540 \text{ in}^2$ (correct answer)
2. $360 \text{ in}^2$
3. $585 \text{ in}^2$
4. $240 \text{ in}^2$

Explanation: Original area = base × height = 20 × 12 = 240 in². When linear dimensions scale by 1.5, area scales by 1.5² = 2.25. New area = 240 × 2.25 = 540 in². B scales by 1.5 only (incorrect). C uses slant side × base (wrong formula). D is original area.

Question 4

1. $52 \text{ cm}$ (correct answer)
2. $68 \text{ cm}$
3. $48 \text{ cm}$
4. $120 \text{ cm}$

Explanation: Diagonals of a rhombus bisect each other at right angles, forming 4 right triangles with legs 12 and 5. Each side = $\sqrt{12^2+5^2} = \sqrt{169} = 13$ cm. Perimeter = 4 × 13 = 52 cm. B uses diagonals as sides. C uses wrong half-lengths. D is the area formula result.

Question 5

1. $54.1 \text{ in}^2$ (correct answer)
2. $14.0 \text{ in}^2$
3. $74.2 \text{ in}^2$
4. $113.1 \text{ in}^2$

Explanation: Circle area = $\pi(10)^2 = 314$ in². Regular hexagon inscribed in circle of radius r has area $\frac{3\sqrt{3}}{2}r^2 = \frac{3\sqrt{3}}{2}(100) \approx 259.8$ in². Shaded = 314 − 259.8 = 54.2 ≈ 54.1 in². B uses wrong hexagon formula (with apothem). C uses square instead of hexagon. D is half the circle.

Question 6

1. $279 \text{ cm}^2$ (correct answer)
2. $225 \text{ cm}^2$
3. $333 \text{ cm}^2$
4. $171 \text{ cm}^2$

Explanation: Hypotenuse = $\sqrt{9^2+12^2} = \sqrt{225} = 15$ cm. Square area = 15² = 225 cm². Triangle area = $\frac{1}{2}(9)(12) = 54$ cm². Total = 225 + 54 = 279 cm². B forgets the triangle. C uses wrong hypotenuse (21). D uses (9+12)² − 225.

Question 7

1. 68 sq ft
2. 72 sq ft
3. 84 sq ft (correct answer)
4. 96 sq ft

Explanation: Split the L-shape into two rectangles: top rectangle is 8 ft × 6 ft = 48 sq ft; bottom rectangle is 6 ft × 6 ft = 36 sq ft. Total area = 48 + 36 = 84 sq ft. A: 68 results from calculation errors. B: 72 omits part of one rectangle. D: 96 assumes the full outer bounding rectangle without subtracting the missing corner.

Question 8

1. 78 ft (correct answer)
2. 60 ft
3. 48 ft
4. 72 ft

Explanation: Perimeter questions test your understanding of the distance around a shape's boundary. When you see a rectangular garden or similar figure, you need to add up all four sides to find the total perimeter. For a rectangle, the perimeter formula is: $P = 2l + 2w$ where $l$ is length and $w$ is width. This works because rectangles have two pairs of equal sides. With a length of 24 feet and width of 15 feet, you calculate: $P = 2(24) + 2(15) = 48 + 30 = 78$ feet. Looking at the wrong answers: Choice B (60 ft) likely comes from incorrectly adding 24 + 15 + 15 + 6, possibly misremembering one of the dimensions. Choice C (48 ft) is a common trap—this is what you get if you only double the length ($2 × 24 = 48$) and forget to include the width at all. Choice D (72 ft) might result from doubling just one dimension incorrectly, such as calculating $2(24) + 2(12)$ if you misread 15 as 12. The correct answer is A (78 ft). Remember this key strategy: For rectangle perimeter problems, always double-check that you're adding all four sides. Either use the formula $P = 2l + 2w$ or manually add $l + w + l + w$. Both methods should give you the same answer, so if they don't match, you know to recalculate before selecting your answer.

Question 9

1. 28.3 m
2. 56.5 m (correct answer)
3. 113.0 m
4. 254.5 m

Explanation: When you encounter a question about the circumference of a circle, you're working with one of geometry's most fundamental formulas. The circumference is the distance around the outside of a circle, and it's calculated using the formula $C = 2\pi r$, where $r$ is the radius. With a radius of 9 meters and $\pi \approx 3.14$, you substitute these values: $C = 2 \times 3.14 \times 9 = 6.28 \times 9 = 56.52$ meters. Rounded to one decimal place, this gives you 56.5 meters, which is answer choice B. Looking at the wrong answers: Choice A (28.3 m) represents a common error where students forget to multiply by 2, calculating only $\pi r$ instead of $2\pi r$. This gives $3.14 \times 9 = 28.26$, which rounds to 28.3. Choice C (113.0 m) likely comes from accidentally using the area formula $A = \pi r^2$ instead of circumference, giving $3.14 \times 9^2 = 3.14 \times 81 = 254.34$, then perhaps dividing by something. Choice D (254.5 m) is exactly what you'd get if you calculated the area using $\pi r^2 = 3.14 \times 81 = 254.34$. Remember this key distinction: circumference uses $2\pi r$ and measures distance around the circle, while area uses $\pi r^2$ and measures space inside the circle. Always double-check which measurement the question is asking for, as mixing up these formulas is one of the most common traps on geometry problems.

Question 10

1. 6 inches
2. 8 inches (correct answer)
3. 10 inches
4. 12 inches

Explanation: The area formula for a trapezoid is A = ½h(b₁ + b₂), where h is the height and b₁, b₂ are the parallel sides. Substituting: 176 = ½h(18 + 26) = ½h(44) = 22h. Solving: h = 176/22 = 8 inches. Choice A (6) would result from using 176 = 6 × 44/2 = 132, not 176. Choice C (10) would give area = 220. Choice D (12) would give area = 264.

Question 11

1. 115.2 square cm
2. 124.8 square cm
3. 138.2 square cm (correct answer)
4. 142.6 square cm

Explanation: The original rhombus has area = ½ × d₁ × d₂ = ½ × 16 × 12 = 96 square cm. When each side is extended by 20%, the rhombus is scaled by a factor of 1.2. Since the diagonals are also scaled by this factor, the new diagonals are 16 × 1.2 = 19.2 cm and 12 × 1.2 = 14.4 cm. The new area = ½ × 19.2 × 14.4 = ½ × 276.48 = 138.24 ≈ 138.2 square cm. Alternatively, since area scales by the square of the linear scale factor: new area = 96 × (1.2)² = 96 × 1.44 = 138.24 square cm. Choice A might result from scaling by 1.2 instead of 1.2². Choice B might come from calculation errors. Choice D might result from incorrect scaling of the diagonals.

Question 12

1. 166.3 square centimeters (correct answer)
2. 172.8 square centimeters
3. 178.4 square centimeters
4. 184.2 square centimeters

Explanation: A regular hexagon with perimeter 48 cm has each side length = 48/6 = 8 cm. The area formula for a regular hexagon with side length s is A = (3√3/2)s². With s = 8: A = (3√3/2)(8)² = (3√3/2)(64) = 96√3. Using √3 ≈ 1.732: A = 96 × 1.732 = 166.272 ≈ 166.3 square cm. Choice B might result from using an incorrect formula. Choice C might come from calculation errors. Choice D might result from using the wrong value for √3.