Math Problem Statement
Solution
The image shows a hexagon with different side lengths and some variables included. We're given:
We are also told that the area of the hexagon is and are asked to find the value of .
Approach to solve for :
-
Divide the hexagon into simpler shapes: The hexagon can be divided into a rectangle and two right-angled triangles (one on the left and one on the right side).
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Area of the rectangle: The rectangle has dimensions:
- Height =
- Width =
So, the area of rectangle is:
-
Area of triangle : This is a right-angled triangle with:
- Base
- Height
The area of triangle is:
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Area of trapezium : Using the trapezium , we can calculate the area based on given data, subtracting any unnecessary elements.
Let's calculate the value of .The value of is approximately .
Would you like further details or clarification on the steps involved?
Here are 5 related questions for practice:
- How would the formula for the area change if had a different length?
- Can you calculate the perimeter of the hexagon for ?
- How does the shape of the hexagon influence the calculation of its area?
- What would happen to the total area if one side of the hexagon was increased by 5 cm?
- How would you find the height of the hexagon if it was irregular?
Tip: For irregular polygons, dividing the shape into simpler geometric forms can make area calculations easier.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Area Calculation
Formulas
Area of a rectangle: A = length * width
Area of a triangle: A = 1/2 * base * height
Area of a hexagon by dividing it into simpler shapes
Theorems
-
Suitable Grade Level
Grades 10-12
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