iGCSE Mathematics (0580) - C5.2 Area and perimeter- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
Start by finding the area of the central square:
$\text{Square Area} = 7.8 \times 7.8 = 60.84 \text{ cm}^2$
Next, determine the height of one of the isosceles triangles by using the total width. The two triangle heights plus the square width equal $14 \text{ cm}$:
$\text{Triangle Height} = (14 – 7.8) / 2 = 3.1 \text{ cm}$
Now, calculate the total area of the $4$ congruent triangles:
$\text{Total Triangle Area} = 4 \times (\frac{1}{2} \times 7.8 \times 3.1) = 48.36 \text{ cm}^2$
Finally, add both areas together to find the total area of the composite shape:
$\text{Total Area} = 60.84 + 48.36 = 109.2 \text{ cm}^2$
✅ Answer: $109.2 \text{ cm}^2$
$\text{Square Area} = 7.8 \times 7.8 = 60.84 \text{ cm}^2$
Next, determine the height of one of the isosceles triangles by using the total width. The two triangle heights plus the square width equal $14 \text{ cm}$:
$\text{Triangle Height} = (14 – 7.8) / 2 = 3.1 \text{ cm}$
Now, calculate the total area of the $4$ congruent triangles:
$\text{Total Triangle Area} = 4 \times (\frac{1}{2} \times 7.8 \times 3.1) = 48.36 \text{ cm}^2$
Finally, add both areas together to find the total area of the composite shape:
$\text{Total Area} = 60.84 + 48.36 = 109.2 \text{ cm}^2$
✅ Answer: $109.2 \text{ cm}^2$
▶️ Answer/Explanation
(a)
A cube has 6 identical square faces. Find the area of one face:
$121.5 \div 6 = 20.25$ cm$^2$
The side length is the square root of the face area: $\sqrt{20.25} = 4.5$ cm
✅ Answer: $4.5$ cm
(b)
(i) Use the formula for the area of a trapezium: Area = $\frac{1}{2}(a+b)h$
$106.25 = \frac{1}{2}(10 + 15) \times h$
$106.25 = 12.5 \times h \implies h = \frac{106.25}{12.5} = 8.5$ cm
✅ Answer: $8.5$ cm
(ii) To convert cm$^2$ to m$^2$, divide by $10,000$ (since $1 \text{ m} = 100 \text{ cm}$, $1 \text{ m}^2 = 10,000 \text{ cm}^2$):
$106.25 \div 10000 = 0.010625$ m$^2$
✅ Answer: $0.010625$ m$^2$