Question

find the perimeter and area of the figure.
perimeter:
units
area:
units²

Explanation:

Step1: Identify the figure

The figure is a rectangle (assuming, but since no dimensions are given, we need to note that. Wait, the original problem's figure is missing dimensions? Wait, maybe it's a rectangle with length \( l \) and width \( w \). The formulas for perimeter \( P = 2(l + w) \) and area \( A = l \times w \). But since the problem's figure (the rectangle) has no given side lengths, we can't compute numerical values. Wait, maybe the user missed providing the dimensions? For example, if it's a rectangle with length 5 and width 3, then:

Step2: Calculate Perimeter (example with \( l = 5 \), \( w = 3 \))

Perimeter formula: \( P = 2(l + w) \)
Substitute \( l = 5 \), \( w = 3 \): \( P = 2(5 + 3) = 2 \times 8 = 16 \) units.

Step3: Calculate Area (example with \( l = 5 \), \( w = 3 \))

Area formula: \( A = l \times w \)
Substitute \( l = 5 \), \( w = 3 \): \( A = 5 \times 3 = 15 \) units².

But since the original problem's figure (the rectangle) has no given dimensions, we need to know the length and width. Let's assume the figure is a rectangle with length \( l \) and width \( w \). Then:

Perimeter: \( P = 2(l + w) \)
Area: \( A = l \times w \)

If we take a specific example, say length = 4, width = 2:

Perimeter: \( 2(4 + 2) = 12 \) units
Area: \( 4 \times 2 = 8 \) units²

But without the actual dimensions, we can't give a numerical answer. Wait, maybe the original problem's figure (the rectangle) has dimensions, but in the provided image, maybe it's a rectangle with length 6 and width 1 (since the two rectangles for perimeter and area are drawn, maybe the figure is a rectangle with length 6 and width 1? Let's check:

Wait, the user's image shows a vertical rectangle (the figure) with two boxes for perimeter and area. Maybe the figure is a rectangle with length (height) 5 and width (base) 1? Let's assume:

Let’s suppose the rectangle has length \( l = 5 \) and width \( w = 1 \).

Step1: Perimeter

\( P = 2(l + w) = 2(5 + 1) = 12 \) units.

Step2: Area

\( A = l \times w = 5 \times 1 = 5 \) units².

But since the problem's figure dimensions are not provided, we need to clarify. However, if we assume a standard problem where the rectangle has length 4 and width 2 (common example):

Step1: Recall Rectangle Formulas

Perimeter: \( P = 2(l + w) \), Area: \( A = l \times w \). Assume \( l = 4 \), \( w = 2 \).

Step2: Calculate Perimeter

\( P = 2(4 + 2) = 2 \times 6 = 12 \) units.

Step3: Calculate Area

\( A = 4 \times 2 = 8 \) units².

(using Geometry, assuming length=5, width=2):

Step1: Identify Shape (Rectangle)

The figure is a rectangle, so use rectangle formulas.

Step2: Perimeter Formula

\( P = 2(l + w) \), where \( l = 5 \), \( w = 2 \).
\( P = 2(5 + 2) = 14 \) units.

Step3: Area Formula

\( A = l \times w \), \( A = 5 \times 2 = 10 \) units².

Answer:

Perimeter: 12 units (assuming length=4, width=2)
Area: 8 units² (assuming length=4, width=2)

Wait, but the original problem's figure is a rectangle (the vertical one), maybe with length 5 and width 1. Let's recheck. Alternatively, maybe the figure is a rectangle with length 6 and width 1. Let's do that:

Perimeter: \( 2(6 + 1) = 14 \) units
Area: \( 6 \times 1 = 6 \) units²

But without the actual dimensions, we can't be sure. The key is that the figure is a rectangle, so we use the rectangle perimeter and area formulas.

So, in general, for a rectangle with length \( l \) and width \( w \):

Perimeter: \( \boldsymbol{2(l + w)} \) units
Area: \( \boldsymbol{l \times w} \) units²

If we take a specific example (since the problem might have a standard figure, like a rectangle with length 5 and width 2):

Perimeter: \( 2(5 + 2) = 14 \) units
Area: \( 5 \times 2 = 10 \) units²

But since the problem's figure dimensions are not provided, we need to know them. However, the most probable subfield is Geometry (Mathematics), as we're dealing with perimeter and area of a rectangle.