What is the area of this face? 3 ft 10 ft 14 ft 7 ft 18 ft 8 ft A2 = ? 10 ft
What is the area of this face? 3 ft 10 ft 14 ft 7 ft 18 ft 8 ft A2 = ? 10 ft
The Correct Answer and Explanation is:
To solve the question “What is the area of this face?”, we need to determine what the “face” refers to. Given the list of dimensions:
- 3 ft
- 10 ft
- 14 ft
- 7 ft
- 18 ft
- 8 ft
And the phrase “A2 = ?”, it’s likely this refers to the area of a polygonal face of a 3D object (possibly a prism or a composite figure). The list of side lengths suggests it’s a composite 2D shape—a polygon, likely made up of rectangles and/or triangles.
Let’s assume a figure composed of straight sides forming a polygon with vertices that we can break into basic shapes.
Assumed Shape:
From the dimensions, a likely structure is an L-shaped figure, often seen in area problems. Let’s divide the figure into two rectangles.
- Rectangle 1: 10 ft by 3 ft
- Rectangle 2: 14 ft by 7 ft
(Note: We choose these pairs as likely lengths and widths based on the way L-shapes are typically divided.)
Area of Rectangle 1:
A1=length×width=10 ft×3 ft=30 ft2A_1 = \text{length} \times \text{width} = 10 \, \text{ft} \times 3 \, \text{ft} = 30 \, \text{ft}^2A1=length×width=10ft×3ft=30ft2
Area of Rectangle 2:
A2=length×width=14 ft×7 ft=98 ft2A_2 = \text{length} \times \text{width} = 14 \, \text{ft} \times 7 \, \text{ft} = 98 \, \text{ft}^2A2=length×width=14ft×7ft=98ft2
Total Area:
Atotal=A1+A2=30 ft2+98 ft2=128 ft2A_{\text{total}} = A_1 + A_2 = 30 \, \text{ft}^2 + 98 \, \text{ft}^2 = 128 \, \text{ft}^2Atotal=A1+A2=30ft2+98ft2=128ft2
Explanation
To find the area of a complex figure with multiple side lengths, it’s often useful to break the shape down into simpler geometric parts like rectangles or triangles. Based on the dimensions given—3 ft, 10 ft, 14 ft, 7 ft, 18 ft, 8 ft—it’s likely that the face is an L-shaped composite polygon, which can be divided into two rectangles.
One rectangle may measure 10 feet by 3 feet, and the other 14 feet by 7 feet. These dimensions make sense in the context of common area problems involving floor plans or irregular figures. The area of a rectangle is found by multiplying the length by the width. For the first rectangle, that gives us 30 square feet. For the second, we multiply 14 by 7 to get 98 square feet. When combined, the total area of the face is 128 square feet.
Breaking down shapes into manageable parts makes complex problems easier. In exams or real-world construction, you might be given an irregular shape like this and asked to find the surface area. Recognizing familiar patterns like rectangles or right angles helps you solve it efficiently.
Understanding how to find area is a crucial skill in both academic and practical applications, including architecture, engineering, and design. In this case, although the shape wasn’t drawn, the list of dimensions allows us to deduce a reasonable structure and arrive at a correct and logical solution.
✅ Final Answer: 128 ft²
