Area and Volume Unit Test

Question

3 of 143 of 14 Items
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:

\[ \boxed{36} \text{ square units} \]