Area of Right Triangles - Free Printable

Problem Analysis

The task involves analyzing the given triangles labeled a, b, c, d, e, f, g, h and determining their areas. The grid provides a reference for measuring the dimensions of each triangle. We will use the formula for the area of a triangle:

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

Each triangle's base and height can be determined by counting the number of grid units along the respective axes.

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Step-by-Step Solution

#### Triangle a
- Base: 4 units (horizontal)
- Height: 3 units (vertical)
- Area:
\[
\text{Area}_a = \frac{1}{2} \times 4 \times 3 = 6
\]

#### Triangle b
- Base: 3 units (horizontal)
- Height: 3 units (vertical)
- Area:
\[
\text{Area}_b = \frac{1}{2} \times 3 \times 3 = 4.5
\]

#### Triangle c
- Base: 4 units (horizontal)
- Height: 2 units (vertical)
- Area:
\[
\text{Area}_c = \frac{1}{2} \times 4 \times 2 = 4
\]

#### Triangle d
- Base: 5 units (horizontal)
- Height: 2 units (vertical)
- Area:
\[
\text{Area}_d = \frac{1}{2} \times 5 \times 2 = 5
\]

#### Triangle e
- Base: 4 units (horizontal)
- Height: 3 units (vertical)
- Area:
\[
\text{Area}_e = \frac{1}{2} \times 4 \times 3 = 6
\]

#### Triangle f
- Base: 2 units (horizontal)
- Height: 3 units (vertical)
- Area:
\[
\text{Area}_f = \frac{1}{2} \times 2 \times 3 = 3
\]

#### Triangle g
- Base: 5 units (horizontal)
- Height: 1 unit (vertical)
- Area:
\[
\text{Area}_g = \frac{1}{2} \times 5 \times 1 = 2.5
\]

#### Triangle h
- Base: 5 units (horizontal)
- Height: 2 units (vertical)
- Area:
\[
\text{Area}_h = \frac{1}{2} \times 5 \times 2 = 5
\]

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Final Areas

Summarizing the areas of all the triangles:

\[
\begin{aligned}
&\text{Area}_a = 6 \\
&\text{Area}_b = 4.5 \\
&\text{Area}_c = 4 \\
&\text{Area}_d = 5 \\
&\text{Area}_e = 6 \\
&\text{Area}_f = 3 \\
&\text{Area}_g = 2.5 \\
&\text{Area}_h = 5 \\
\end{aligned}
\]

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Final Answer

\[
\boxed{6, 4.5, 4, 5, 6, 3, 2.5, 5}
\]