Let's solve each triangle's area step by step using the formula:
>
Area of a triangle = ½ × base × height
We’ll go through each part (a to f) one by one.
---
a.
Given:
- Base = 4 cm
- Height (h) = 6 cm
$$
\text{Area} = \frac{1}{2} \times 4 \times 6 = 12 \, \text{cm}^2
$$
✔ Already solved in the image:
12 sq cm
---
b.
Given:
- Base = 6 cm
- Height (h) = 8 cm (the dotted line from top vertex to base)
$$
\text{Area} = \frac{1}{2} \times 6 \times 8 = 24 \, \text{cm}^2
$$
✔ Answer: 24 sq cm
---
c.
Given:
- Base = 8 cm
- Height (h) = 9 cm (dotted line from vertex to base)
Note: The two sides are 10 cm and 10 cm, but we don’t need them since we have base and height.
$$
\text{Area} = \frac{1}{2} \times 8 \times 9 = 36 \, \text{cm}^2
$$
✔ Answer: 36 sq cm
---
d.
Given:
- All sides = 10 cm → equilateral triangle
- Height (h) = 6 cm
- Base = 10 cm (since it’s the side on which the height is drawn)
$$
\text{Area} = \frac{1}{2} \times 10 \times 6 = 30 \, \text{cm}^2
$$
✔ Answer: 30 sq cm
---
e.
Given:
- Base = 6 cm
- Height (h) = 7 cm (dotted perpendicular line)
$$
\text{Area} = \frac{1}{2} \times 6 \times 7 = 21 \, \text{cm}^2
$$
✔ Answer: 21 sq cm
---
f.
Given:
- Base = 6 cm
- Height (h) = 6 cm (dotted line from top vertex to base)
$$
\text{Area} = \frac{1}{2} \times 6 \times 6 = 18 \, \text{cm}^2
$$
✔ Answer: 18 sq cm
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✔ Final Answers:
| Part | Area |
|------|------|
| a | 12 cm² |
| b | 24 cm² |
| c | 36 cm² |
| d | 30 cm² |
| e | 21 cm² |
| f | 18 cm² |
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🔍 Explanation:
The key idea is that for
any triangle, as long as you know:
- The
base (any side)
- The
height (perpendicular distance from the base to the opposite vertex)
You can use:
> $$
> \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
> $$
Even if the triangle is tilted or not right-angled, this formula works — just make sure the height is
perpendicular to the base.
In some cases (like b), the height is not along a side but shown with a dotted line — that’s fine, as long as it's perpendicular.
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Let me know if you'd like this explained visually or want practice problems! 😊
Parent Tip: Review the logic above to help your child master the concept of area of triangles worksheet.
