7TH MATHS PERIMETER AND AREA OF THE RHOMBUS

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Perimeter & Area of a Rhombus – Master Quiz

1. A piece of wire is bent to form a rhombus with a side length of 's'. Which mathematical expression represents the total length of the wire used?

a) 2 × (s + s) b) 4 × s c) s × s d) (diagonal 1 × diagonal 2) / 2

Correct Answer: b) 4 × s

Explanation: The total length of the wire is the perimeter of the rhombus. Since a rhombus has four equal sides, the perimeter formula is simply 4 multiplied by the side length (4 × s).

2. A rhombus-shaped floor tile has a total perimeter of 24 cm. If you want to paint a decorative line exactly along just ONE of its edges, how long must that painted line be?

a) 12 cm b) 8 cm c) 6 cm d) 4 cm

Correct Answer: c) 6 cm

Explanation: The perimeter (all 4 sides added together) is 24 cm. To find the length of one single edge, divide the perimeter by 4. 24 ÷ 4 = 6 cm.

3. A garden is shaped like a rhombus with a total outer boundary (perimeter) of 40 meters. What is the length of each side of the garden?

a) 8 m b) 10 m c) 12 m d) 20 m

Correct Answer: b) 10 m

Explanation: Perimeter = 4 × side. So, 40 m = 4 × side. By dividing 40 by 4, we find that each side of the garden is exactly 10 meters long.

4. A kite is shaped perfectly like a rhombus with all four sides equal to 9.5 cm. How much string is needed to completely outline its outer boundary?

a) 19 cm b) 28.5 cm c) 38 cm d) 40 cm

Correct Answer: c) 38 cm

Explanation: The outer boundary is the perimeter. Perimeter = 4 × 9.5 cm. 9.5 + 9.5 + 9.5 + 9.5 = 38 cm.

5. If just one side of a rhombus measures 7.25 cm, what is the combined sum of all its sides?

a) 28 cm b) 29 cm c) 30 cm d) 29.5 cm

Correct Answer: b) 29 cm

Explanation: The combined sum of all sides is the perimeter. Multiply 7.25 cm by 4. (7 × 4 = 28) and (0.25 × 4 = 1). 28 + 1 = 29 cm.

6. To find the amount of flat space inside a rhombus, a student multiplies the lengths of its two intersecting diagonals and then divides the final result by 2. Is this mathematical method correct?

a) No, they must multiply base by height instead. b) Yes, this perfectly describes the area formula: ½ × (d1 × d2). c) No, they should multiply the side by itself. d) Yes, but only if the rhombus is a perfect square.

Correct Answer: b) Yes, this perfectly describes the area formula: ½ × (d1 × d2).

Explanation: The area of any rhombus can be found by taking the product of its two diagonals and dividing by two. (Base × height is also valid, but the student's diagonal method is 100% correct).

7. A rhombus has two diagonals measuring 10 cm and 8 cm. What is the total area covered by this geometric shape?

a) 80 cm² b) 18 cm² c) 40 cm² d) 100 cm²

Correct Answer: c) 40 cm²

Explanation: Area = ½ × (diagonal 1 × diagonal 2).
Area = ½ × (10 cm × 8 cm) = ½ × 80 cm² = 40 cm².

8. The diagonals of a paper rhombus are 12 cm and 16 cm. If you cut the rhombus into four separate triangles along its intersecting diagonal lines, what is the combined total area of all four triangles?

a) 192 cm² b) 96 cm² c) 48 cm² d) 72 cm²

Correct Answer: b) 96 cm²

Explanation: The combined area of those four triangles is exactly equal to the area of the original rhombus! Area = ½ × (12 × 16) = ½ × 192 = 96 cm².

9. A rhombus has an area of exactly 140 cm². If one of its inner diagonals measures 20 cm, what MUST be the length of the other diagonal?

a) 14 cm b) 7 cm c) 28 cm d) 280 cm

Correct Answer: a) 14 cm

Explanation: We work backward from the area formula: 140 = ½ × (20 × d2).
140 = 10 × d2.
Divide both sides by 10, leaving d2 = 14 cm.

10. A stained glass window is shaped like a rhombus. Its vertical diagonal is 18 cm and its horizontal diagonal is 24 cm. Exactly how much colored glass is needed to fill this window?

a) 108 cm² b) 432 cm² c) 216 cm² d) 360 cm²

Correct Answer: c) 216 cm²

Explanation: The amount of glass required is equal to the area of the window. Area = ½ × (18 × 24) = ½ × 432 = 216 cm².