Middle School Math Quiz: Area Of Polygons And Composites
4 questions · exam conditions
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Area Of Polygons And CompositesQuestion 1 of 4

A regular hexagon is divided into 6 congruent triangular sections. If each triangular section has an area of 15.6 square centimeters, and a circular hole with radius 2 cm is cut from the center of the hexagon, what is the area of the remaining figure? (Use π ≈ 3.14)

81.04 cm²
85.04 cm²
89.04 cm²
93.04 cm²
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Middle School Math Quiz

Middle School Math Quiz: Area Of Polygons And Composites

Practice Area Of Polygons And Composites in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Area Of Polygons And Composites, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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All questions

Question 1

A regular hexagon is divided into 6 congruent triangular sections. If each triangular section has an area of 15.6 square centimeters, and a circular hole with radius 2 cm is cut from the center of the hexagon, what is the area of the remaining figure? (Use π ≈ 3.14)

  1. 81.04 cm² (correct answer)
  2. 85.04 cm²
  3. 89.04 cm²
  4. 93.04 cm²
Explanation: The total area of the hexagon is 6 × 15.6 = 93.6 cm². The area of the circular hole is πr² = 3.14 × 2² = 3.14 × 4 = 12.56 cm². The remaining area is 93.6 - 12.56 = 81.04 cm². Choice B (85.04) might result from using radius 1.5 cm for the hole. Choice C (89.04) might result from using a hole area of 4.56 cm². Choice D (93.04) might result from using a hole area of only 0.56 cm².

Question 2

A trapezoid has parallel bases of lengths 14 meters and 8 meters. If the area of the trapezoid is 132 square meters, and a rectangular section with width equal to the shorter base is removed from the center, what is the area of the remaining figure when the height of the removed rectangle is 3 meters?

  1. 108 square meters (correct answer)
  2. 114 square meters
  3. 120 square meters
  4. 126 square meters
Explanation: First, find the height of the trapezoid using the area formula: Area = (1/2)(b₁ + b₂)h, so 132 = (1/2)(14 + 8)h = (1/2)(22)h = 11h. Therefore h = 12 meters. The removed rectangle has width 8 meters (shorter base) and height 3 meters, so its area = 8 × 3 = 24 square meters. The remaining area = 132 - 24 = 108 square meters. Choice B (114) might result from using height 2 for the rectangle. Choice C (120) might result from removing a 3×4 rectangle. Choice D (126) might result from removing only a 2×3 rectangle.

Question 3

A parallelogram has a base of 16 inches and a height of 9 inches. Three congruent triangular pieces, each with area 18 square inches, are cut out from the parallelogram. What percentage of the original parallelogram area remains?

  1. 52.5%
  2. 62.5% (correct answer)
  3. 67.5%
  4. 72.5%
Explanation: The area of the parallelogram is base × height = 16 × 9 = 144 square inches. Three triangular pieces with area 18 square inches each are removed, so total removed area = 3 × 18 = 54 square inches. Remaining area = 144 - 54 = 90 square inches. Percentage remaining = (90/144) × 100% = 62.5%. Choice A (52.5%) results from removing 68 sq in instead of 54. Choice C (67.5%) results from removing 47 sq in. Choice D (72.5%) results from removing 40 sq in.

Question 4

A rhombus has diagonals of length 18 cm and 24 cm. If two identical right triangles are removed from opposite corners, each with legs of length 3 cm and 4 cm, what is the area of the remaining figure?

  1. 198 cm²
  2. 204 cm² (correct answer)
  3. 210 cm²
  4. 216 cm²
Explanation: The area of a rhombus is (1/2) × d₁ × d₂ = (1/2) × 18 × 24 = 216 cm². Each right triangle has area (1/2) × 3 × 4 = 6 cm². Since two triangles are removed, total removed area = 2 × 6 = 12 cm². Remaining area = 216 - 12 = 204 cm². Choice A (198) results from removing 18 cm² instead of 12. Choice C (210) results from removing only 6 cm². Choice D (216) results from not removing any area.