2.

Question

Find the area of this irregular figure. All angles are right angles.

296 in2

128 in2

80 in2

256 in2

Answer 1

In order to find the area of an irregular figure where all angles are right angles, one effective method is to divide the figure into smaller rectangles or squares. After determining the areas of these smaller shapes, you can sum them to find the total area of the figure. Let me go through a general process, but it’s important to have the specific dimensions of each section of the irregular figure to use this method accurately.

Here is a step-by-step outline of how you can approach this:

1. **Divide the Figure**: Break down the irregular figure into a combination of rectangles and squares. Each shape should have right angles as indicated.

2. **Measure Dimensions**: Obtain the lengths and widths of each of these smaller rectangles/squares.

3. **Calculate Individual Areas**: Use the formula for the area of a rectangle (Area = Length × Width) to find the area of each section.

4. **Sum the Areas**: Add together the areas of all the smaller sections to get the total area.

Let's assume we have an irregular figure and you have the dimensions (note that without seeing the actual figure, I'll provide just an illustrative example):

Imagine an L-shaped figure, which can be divided into two rectangles. Suppose you have the following dimensions for these rectangles:
- Rectangle 1: Length = 10 inches, Width = 8 inches.
- Rectangle 2: Length = 10 inches, Width = 5 inches.

1. **Find the area of Rectangle 1**:
\( \text{Area}_1 = 10 \, \text{in} \times 8 \, \text{in} = 80 \, \text{in}^2 \)

2. **Find the area of Rectangle 2**:
\( \text{Area}_2 = 10 \, \text{in} \times 5 \, \text{in} = 50 \, \text{in}^2 \)

3. **Add the areas**:
\( \text{Total Area} = \text{Area}_1 + \text{Area}_2 = 80 \, \text{in}^2 + 50 \, \text{in}^2 = 130 \, \text{in}^2 \)

Since every problem needs precise dimensions for accuracy, replace the measurements in the example with the actual dimensions from the figure you have.

Once divided adequately and areas calculated as per the outlined steps, you should compare the calculated total area to the given options to find the correct answer. The possible answers given are 296 in², 128 in², 80 in², and 256 in².

Without specifying the exact measurements from the figure you provided, it is impossible to definitively conclude which one is correct. But with this method, you should be able to determine the area accurately.