Geometric Composition of the Shape
The problem describes a shape formed by arranging 6 regular hexagons around a common center. These hexagons fit together perfectly without any gaps.
Area Relationship
The total area of the combined shape is the sum of the areas of the individual regular hexagons that compose it.
- Let the area of one regular hexagon be denoted by $A_h$.
- The combined shape is made up of exactly 6 such regular hexagons.
- Therefore, the total area of the combined shape, $A_{total}$, is $6 \times A_h$.
Calculating the Area Ratio
The question asks for the ratio of the area of the combined shape to the area of one hexagon.
Ratio = $\frac{\text{Area of Combined Shape}}{\text{Area of One Hexagon}}$
Substituting the areas:
Ratio = $\frac{A_{total}}{A_h} = \frac{6 \times A_h}{A_h}$
Simplifying the expression, the $A_h$ terms cancel out:
Ratio = $\frac{6}{1}$
This means the ratio is 6:1.
Similar Questions
- An L-shaped floor is made of two rectangles (6 m $\times$ 4 m and 8 m $\times$ 6 m). Tiles cost ₹450/$m^2$, but a 10% discount is given if more than 70 $m^2$ is tiled. What is the total cost after discount?
- A triangular traffic sign has sides measuring 13 m, 14 m, and 15 m. If the cost to paint the sign is ₹5 per square meter, what will be the total expense to paint the entire sign?
- A triangular field with base 40 m and height 30 m shares a side with a rectangle of length 40 m and breadth 25 m. Find the combined area and percentage of the triangle’s area in the total.
- A regular hexagon is inscribed inside a circle of radius 14 cm. Find the area of the hexagon.
- A steel plate is in the shape of a right triangle. The lengths of the legs are in the ratio 5:12. If the hypotenuse is 13 m, what is the area?
- A triangular flag has base and height in the ratio 5:4. If the area is 160 cm², what are the base and height?
- Consider a right trapezoidal field. Its two parallel sides are 30 meters and 50 meters long. One of its non-parallel sides, which acts as the height, measures 20 meters. What is the area of this field?
- A hexagon is drawn inside a circle with a radius of 21 cm. Determine the approximate area of the hexagon.
- A rectangular field has an area of 600 square meters. If its length were increased by 10 meters and its width decreased by 2 meters, the area of the field would remain the same. Find the original dimensions (length and width) of the field.
- A garden is in the shape of a regular hexagon, each side 20 m. If 5% of it is occupied by a circular fountain, find the remaining area.
Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
