Math worksheet for calculating the area of non-right angled triangles using grid paper and given dimensions.

Let's solve the problem step by step.

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🔷 Overview

We are asked to find the area of non-right-angled triangles using two methods:
1. Section A: Triangles drawn on a 1-inch squared grid — we can use counting squares or the formula.
2. Section B: Triangles with labeled base and height (or other sides) — use the standard triangle area formula.

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## ✔ Formula for Area of a Triangle
$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$
> The height must be perpendicular to the base.

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# 🔹 Section A: Grid-Based Triangles

Each square is 1 inch × 1 inch, so we can count units.

We’ll use the formula with base and height measured from the grid.

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🔸 1)

- Base: From left to right → spans 5 inches
- Height: Vertical distance from base to top vertex → 4 inches
- Area = $ \frac{1}{2} \times 5 \times 4 = 10 $ in²

✔ Answer: 10 in²

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🔸 2)

- Base: Horizontal line at bottom → spans 8 inches
- Height: Vertical distance from base to peak → 3 inches
- Area = $ \frac{1}{2} \times 8 \times 3 = 12 $ in²

✔ Answer: 12 in²

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🔸 3)

This one is upside down, but same idea.

- Base: Bottom side → spans 6 inches
- Height: Vertical distance from base to top point → 5 inches
- Area = $ \frac{1}{2} \times 6 \times 5 = 15 $ in²

✔ Answer: 15 in²

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🔸 4)

- Base: Horizontal side → spans 6 inches
- Height: Perpendicular from opposite vertex → 4 inches
- Area = $ \frac{1}{2} \times 6 \times 4 = 12 $ in²

✔ Answer: 12 in²

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🔸 5)

- Base: Horizontal side → spans 7 inches
- Height: Perpendicular from top vertex → 4 inches
- Area = $ \frac{1}{2} \times 7 \times 4 = 14 $ in²

✔ Answer: 14 in²

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## ✔ Section A Summary:
| Problem | Area (in²) |
|--------|------------|
| 1 | 10 |
| 2 | 12 |
| 3 | 15 |
| 4 | 12 |
| 5 | 14 |

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# 🔹 Section B: Labeled Triangles

Use the formula again:
$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

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🔸 1)

- Base = 10 in
- Height = 7 in (perpendicular)
- Area = $ \frac{1}{2} \times 10 \times 7 = 35 $ in²

✔ Answer: 35 in²

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🔸 2)

- Base = 4 in
- Height = 12 in (dashed line shows it’s perpendicular)
- Area = $ \frac{1}{2} \times 4 \times 12 = 24 $ in²

✔ Answer: 24 in²

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🔸 3)

- Base = 14 in
- Height = 8 in (dashed line shows it’s perpendicular to the 14-in side)
- Area = $ \frac{1}{2} \times 14 \times 8 = 56 $ in²

✔ Answer: 56 in²

> Note: The 9 in side is not used — it’s just another side.

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🔸 4)

- Base = 2 in
- Height = 9 in (perpendicular dashed line)
- Area = $ \frac{1}{2} \times 2 \times 9 = 9 $ in²

✔ Answer: 9 in²

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🔸 5)

- Base = 20 in (horizontal side)
- Height = 6 in (vertical dashed line from opposite vertex)
- Area = $ \frac{1}{2} \times 20 \times 6 = 60 $ in²

✔ Answer: 60 in²

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🔸 6)

- Base = 5 in
- Height = 8 in (dashed line perpendicular to base)
- Area = $ \frac{1}{2} \times 5 \times 8 = 20 $ in²

✔ Answer: 20 in²

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## ✔ Section B Summary:
| Problem | Area (in²) |
|--------|------------|
| 1 | 35 |
| 2 | 24 |
| 3 | 56 |
| 4 | 9 |
| 5 | 60 |
| 6 | 20 |

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## 📌 Final Answers:

✔ Section A:

1) 10 in²
2) 12 in²
3) 15 in²
4) 12 in²
5) 14 in²

✔ Section B:

1) 35 in²
2) 24 in²
3) 56 in²
4) 9 in²
5) 60 in²
6) 20 in²

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✔ Key Tips:

- Always make sure the height is perpendicular to the base.
- On grid paper, count squares or use coordinates to measure base and height.
- Units matter! Always include in².

Let me know if you'd like this as a printable answer sheet!