Let's solve
Question 1 and
Question 2 step by step.
---
🔷 Formula for the Area of a Triangle
The area of a triangle is given by:
$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$
Where:
- The
base is one side of the triangle.
- The
height is the perpendicular distance from the base to the opposite vertex.
We’ll use this formula for all parts.
---
##
✔ Question 1: Find the area of each triangle.
All these are
right-angled triangles, so we can use the two perpendicular sides as base and height.
---
(a)
Given:
- Base = 6 cm
- Height = 8 cm
$$
\text{Area} = \frac{1}{2} \times 6 \times 8 = 3 \times 8 = 24\, \text{cm}^2
$$
✔ Answer: 24 cm²
---
(b)
Given:
- Base = 7 cm
- Height = 4 cm
$$
\text{Area} = \frac{1}{2} \times 7 \times 4 = \frac{28}{2} = 14\, \text{cm}^2
$$
✔ Answer: 14 cm²
---
(c)
Given:
- Base = 5 cm
- Height = 12 cm
$$
\text{Area} = \frac{1}{2} \times 5 \times 12 = \frac{60}{2} = 30\, \text{cm}^2
$$
✔ Answer: 30 cm²
---
(d)
Given:
- Base = 20 cm
- Height = 4 cm
$$
\text{Area} = \frac{1}{2} \times 20 \times 4 = 10 \times 4 = 40\, \text{cm}^2
$$
✔ Answer: 40 cm²
---
(e)
Given:
- Base = 9 cm
- Height = 6 cm
$$
\text{Area} = \frac{1}{2} \times 9 \times 6 = \frac{54}{2} = 27\, \text{cm}^2
$$
✔ Answer: 27 cm²
---
(f)
Given:
- Base = 13 cm
- Height = 10 cm
$$
\text{Area} = \frac{1}{2} \times 13 \times 10 = \frac{130}{2} = 65\, \text{cm}^2
$$
✔ Answer: 65 cm²
---
##
✔ Question 2: Find the area of each triangle.
These triangles are
not necessarily right-angled, but they have a labeled
height (shown as a dotted line), so we can still use the formula.
---
(a)
Given:
- Base = 8 cm (from the base line)
- Height = 6 cm (perpendicular dotted line)
$$
\text{Area} = \frac{1}{2} \times 8 \times 6 = 4 \times 6 = 24\, \text{cm}^2
$$
✔ Answer: 24 cm²
---
(b)
Given:
- Base = 14 cm
- Height = 5 cm
$$
\text{Area} = \frac{1}{2} \times 14 \times 5 = 7 \times 5 = 35\, \text{cm}^2
$$
✔ Answer: 35 cm²
---
(c)
Given:
- Base = 9 cm
- Height = 3 cm
$$
\text{Area} = \frac{1}{2} \times 9 \times 3 = \frac{27}{2} = 13.5\, \text{cm}^2
$$
✔ Answer: 13.5 cm²
---
##
✔ Final Answers:
Question 1:
(a) 24 cm²
(b) 14 cm²
(c) 30 cm²
(d) 40 cm²
(e) 27 cm²
(f) 65 cm²
Question 2:
(a) 24 cm²
(b) 35 cm²
(c) 13.5 cm²
---
💡
Key Tip: Always identify the
base and the
height that are
perpendicular to each other. In right triangles, the two legs are perpendicular, so you can use them directly. In non-right triangles, the height is usually shown as a dotted line with a right angle symbol.
Let me know if you want a diagram explanation or help with any specific part!
Parent Tip: Review the logic above to help your child master the concept of area of triangle worksheet.
