What is the area of the given shape in cm²?
Understand the Problem
The question is asking to calculate the area of a geometric shape, as indicated in the image. The dimensions provided suggest it's likely related to triangle or trapezoid calculations. To solve it, we'll apply the appropriate geometric formulas using the given measurements.
Answer
The area is $126 \, \text{cm}^2$.
Answer for screen readers
The area is $126 , \text{cm}^2$.
Steps to Solve
- Identify the Shape and Dimensions
The shape in the image is a trapezoid, consisting of two triangles with the following dimensions:
- Height (h) = 12 cm
- Base 1 (b1) = 14 cm
- Base 2 (b2) = 7 cm
- The height of the smaller triangle = 3 cm
- Calculate the Area of the Trapezoid
To find the area of the trapezoid, we use the formula:
[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h ]
Substituting (b_1 = 14 , cm), (b_2 = 7 , cm), and (h = 12 , cm):
[ \text{Area} = \frac{1}{2} \times (14 + 7) \times 12 ]
- Perform the Calculation
First, add the bases:
[ 14 + 7 = 21 , cm ]
Now substitute:
[ \text{Area} = \frac{1}{2} \times 21 \times 12 ]
Calculating further:
[ \text{Area} = \frac{1}{2} \times 252 = 126 , cm^2 ]
The area is $126 , \text{cm}^2$.
More Information
The trapezoid formula used here is a key concept in geometry, which allows us to calculate the area efficiently using the bases and height. Trapezoids are common in various fields including architecture and engineering.
Tips
- Forgetting to convert the height to the correct position or dimensions when working with composite shapes.
- Confusing the base and height in the trapezoid formula.
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