GED Mathematical reasoning 2 — Questions and Answers
Question 1: A rectangle has a length of 12 cm and a width of 7 cm. What is its perimeter?
- 19 cm
- 38 cm (Correct answer)
- 84 cm
- 76 cm
Correct answer: 38 cm
Perimeter of a rectangle = 2(length + width) = 2(12 + 7) = 2(19) = 38 cm.
The perimeter of a rectangle is the total length of all four sides.
Formula: P = 2l + 2w = 2(l + w)
where l = length and w = width.
P = 2(12 + 7) = 2(19) = 38 cm
You can also add all four sides directly:
12 + 7 + 12 + 7 = 38 cm ✓
Don't confuse perimeter (distance around) with area (space inside):
• Perimeter = 38 cm (linear measurement)
• Area = 12 × 7 = 84 cm² (square measurement)
Option C (84 cm) is the area, not the perimeter — a common mistake on the GED.
Question 2: Find the area of a triangle with a base of 10 inches and a height of 6 inches.
- 16 sq in
- 30 sq in (Correct answer)
- 60 sq in
- 120 sq in
Correct answer: 30 sq in
Area of triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30 square inches.
The area of a triangle formula is: A = ½ × b × h, where b is the base and h is the perpendicular height.
A = ½ × 10 × 6 = ½ × 60 = 30 square inches.
The formula makes geometric sense: a triangle is half of a parallelogram (or rectangle for right triangles) with the same base and height. If you draw two congruent triangles together along their bases, they form a rectangle of area b × h, so each triangle has area ½bh.
Important: the height must be PERPENDICULAR to the base — it's not necessarily the slant side of the triangle.
Units: area is always expressed in square units (in², cm², ft², etc.).
Question 3: What is the volume of a rectangular box (prism) with length 5 ft, width 4 ft, and height 3 ft?
- 12 ft³
- 47 ft³
- 60 ft³ (Correct answer)
- 120 ft³
Correct answer: 60 ft³
Volume of a rectangular prism = l × w × h = 5 × 4 × 3 = 60 cubic feet.
Volume measures the three-dimensional space inside a solid figure.
For a rectangular prism (box): V = l × w × h
V = 5 × 4 × 3 = 60 ft³
You can think of it as: (area of base) × height = (5 × 4) × 3 = 20 × 3 = 60 ft³.
Volume is expressed in cubic units (ft³, cm³, m³, etc.) because you're multiplying three length measurements.
Real-world application: This box could hold 60 cubic feet of material. If you were filling it with 1-foot cubes, you'd need exactly 60 of them.
Don't confuse with surface area: SA = 2(lw + lh + wh) = 2(20 + 15 + 12) = 2(47) = 94 ft².
Question 4: In a right triangle, the two legs measure 6 cm and 8 cm. What is the length of the hypotenuse?
- 7 cm
- 10 cm (Correct answer)
- 11 cm
- 14 cm
Correct answer: 10 cm
Using the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.
The Pythagorean theorem states that in any right triangle, the sum of the squares of the two legs equals the square of the hypotenuse: a² + b² = c².
c² = 6² + 8² = 36 + 64 = 100
c = √100 = 10 cm
This is a 3-4-5 Pythagorean triple scaled up by 2: (6, 8, 10) = 2×(3, 4, 5). Recognizing common Pythagorean triples saves time on the GED:
• 3-4-5 (and multiples: 6-8-10, 9-12-15)
• 5-12-13
• 8-15-17
The hypotenuse is always the longest side and is opposite the right angle (90° angle). Always check that your answer is larger than both legs.
Question 5: A circular pond has a radius of 7 meters. Using π ≈ 3.14, what is the area of the pond?
- 21.98 m²
- 43.96 m²
- 153.86 m² (Correct answer)
- 615.44 m²
Correct answer: 153.86 m²
Area = π × r² = 3.14 × 7² = 3.14 × 49 = 153.86 m².
The area of a circle is A = πr², where r is the radius.
A = π × r² = 3.14 × 7² = 3.14 × 49 = 153.86 m²
Common mistakes:
• Using diameter instead of radius: if the diameter were 7, r = 3.5, and A = 3.14 × 12.25 ≈ 38.5 m²
• Forgetting to square: 3.14 × 7 = 21.98 (that's approximately the circumference ÷ 2)
Related formula — circumference: C = 2πr = 2 × 3.14 × 7 = 43.96 m (option B is this value)
Memory trick: 'Area = πr²' — think 'a pie are squared' to remember the formula.
Question 6: Two angles of a triangle measure 55° and 72°. What is the measure of the third angle?
- 33°
- 53° (Correct answer)
- 63°
- 127°
Correct answer: 53°
The sum of angles in a triangle is 180°. Third angle = 180° − 55° − 72° = 53°.
The Triangle Angle Sum Theorem states that the interior angles of any triangle always sum to 180°.
Third angle = 180° − 55° − 72° = 180° − 127° = 53°.
Verification: 55° + 72° + 53° = 180° ✓
This is a fundamental geometric property that applies to ALL triangles — equilateral, isosceles, scalene, right, acute, and obtuse.
Note: For polygons with more sides, the angle sum formula is (n − 2) × 180°, where n is the number of sides:
• Triangle (n=3): (3−2) × 180° = 180°
• Quadrilateral (n=4): (4−2) × 180° = 360°
• Pentagon (n=5): (5−2) × 180° = 540°
