a walkway 2 meters wide surrounds a rectangular play area 50 meters long and 30 meters wide. find the area of the walkway.
the answer is 304m^2
The area of a circle is 314sq.cm and area of its minor sector is 31.4sq.cm.find the area of major sector
To find the area of the walkway surrounding the rectangular play area, we first need to calculate the dimensions of the larger rectangle that includes both the play area and the walkway.
Let's start by adding twice the width of the walkway to both the length and width of the play area. This will give us the dimensions of the larger rectangle:
Length of the larger rectangle = Length of the play area + 2 × Width of the walkway
= 50 meters + 2 × 2 meters (since the walkway is 2 meters wide)
= 50 meters + 4 meters
= 54 meters
Width of the larger rectangle = Width of the play area + 2 × Width of the walkway
= 30 meters + 2 × 2 meters
= 30 meters + 4 meters
= 34 meters
Now that we have the dimensions of the larger rectangle, we can calculate its area by multiplying the length by the width:
Area of the walkway + play area = Length of the larger rectangle × Width of the larger rectangle
= 54 meters × 34 meters
= 1836 square meters
Next, we need to subtract the area of just the play area to find the area of the walkway alone. The area of the play area can be calculated as the length of the play area multiplied by the width of the play area:
Area of the play area = Length of the play area × Width of the play area
= 50 meters × 30 meters
= 1500 square meters
Finally, we can calculate the area of the walkway by subtracting the area of the play area from the total area of the walkway and play area:
Area of the walkway = Area of the walkway + play area - Area of the play area
= 1836 square meters - 1500 square meters
= 336 square meters
Therefore, the area of the walkway is 336 square meters.