Area and Volume Unit Test

Question

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Question
Use the image to answer the question.

An illustration shows a 10 by 10 grid. A non-right triangle is enclosed within the grid. The first vertex is at the top of row 2 and the right of column 6. The second vertex is at the top of row 8 and the right of column 1. The third vertex is at the top of row 10 and right of column 10.

What is the area of the non-right triangle? The base and height are found by counting the squares.

Answer 1

To find the area of the non-right triangle, we can use the formula for the area of a triangle:

$$\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$$

First, we need to identify the base and the height of the triangle.

Based on the given coordinates of the vertices:
- Vertex 1 (V1) is at (6, 2).
- Vertex 2 (V2) is at (1, 8).
- Vertex 3 (V3) is at (10, 10).

Let's assume the base of the triangle extends horizontally from V2 to V3 across the bottom of the triangle.

**Base:**
The horizontal distance (base) from V2 (1, 8) to V3 (10, 10) corresponds to the columns they span. The base length is calculated by:
$$\text{base}=10-1=9\text{ units}$$

**Height:**
The height can be measured vertically from V1 (6, 2) to V3 (10, 10). The height length is calculated by:
$$\text{height}=10-2=8\text{ units}$$

Now, substitute the base and height into the area formula:
$$\text{Area}=\frac{1}{2}\times 9\times 8$$
$$\text{Area}=\frac{1}{2}\times 72$$
$$\text{Area}=36\text{ square units}$$

Therefore, the area of the non-right triangle is:

$$\boxed{{\displaystyle 36}}\text{ square units}$$