Questions

Case study (4 Marks)

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4 questions · timed · auto-graded

Question 14 Marks
A zoo is in the shape of an isosceles trapezium.
It is divided into three zones – Zone 1, Zone 2 and Zone 3.
Animals are kept without cages in Zone 1. Zone 2 is for visitors and Zone 3 is reserved for park
authorities. 

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To avoid the entry of animals in zones 2 and 3, a 1.8 km long wired fencing is installed.
7. Which of the following calculations shows the area for animals?
  A. √1.35×0.65×1.15
  B. 2.15×0.35×0.65×1.15
  C. √3.15×1.35×1.65×1.15
  D. √4.30×1.35×0.65×1.15
8. “The area reserved for animals is twice the area reserved for the zoo authorities.” Do you have enough information to support this statement? Explain your answer.

Answer
7. B. 2.15×0.35×0.65×1.15
8. No, with a valid explanation.
● No, we don’t have enough information to say that the area reserved for animals is double the area reserved for the zoo authorities. The area reserved under zone 1 = area reserved under zone 2 + 3, but we cannot say the area reserved under zone 2 and 3 are equal.
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Question 24 Marks
The outer boundary of Zone 1 is made of solid structures in the shape of isosceles triangles of the same size and barbed wires. 

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The wall consists of 15 such solid structures.
9. Which of the following calculations shows the total area (in square meters) of the solid structures?
  A. √50× 50 ×30
  B. √130×50×50×30
  C. 15√130×50×50×30
  D. 15√260×180×180×16
10. What is the area of a triangle with side lengths 20 cm, 20 cm and 8 cm?

Answer
9. C.15√130×50×50×30
10. 32√6cm² 
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Question 34 Marks
Glass buildings can be strengthened using iron frames. A glass structure and its iron frame are
shown below.

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The frame consists of equal triangles. The dimensions of a triangle are shown below.

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1. How much area is enclosed by one triangle?
2. What is the area of part 1 of the frame?
  A. 84 m²
  B. 1680 m²
  C. 3360 m²
  D. 3696 m²
3. Is the area of part 1 equal to the area of part 2? Why?
4. Maintenance of the building’s exterior is done by a company. The company charges Rs 750 per square meter per month.
Which of the following calculations represents the monthly maintenance charges?
  A. 24 × 12
  B. 750 × 24
  C. 3024 × 750
  D. 6720 × 750

Answer
1. 24 m²
2. D. 3696 m²
3. No, with valid reasoning
● No, the area reserved under part 1 is not equal to the area reserved under part 2. Area under part 1 is 3696 m² whereas the area under part 2 is 3024 m²
4. D. 6720×750
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Question 44 Marks
The design on a tile is made of isosceles triangles. 
The side lengths of the triangles are 6 cm, 6 cm and 8 cm. 

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5. How much area of the tile is black?
  A. 24 cm²
  B. 9√7 cm²
  C. 90 cm²
  D. 112√5 cm²
6. A tile is made by joining the vertices of four equilateral triangles. The side length of the triangles is 15 cm. What is the area of the tile? 

Answer
5. D. 112√5 cm²
6. 225√3 square centimetres
225√3 sq cm
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