The perimeter of a quadrilateral pqrs is 30mm and its area is 50mm squered ,find the peremiter and area of quadrilateral pqrs if scale factor is 1/5
area goes up as the square of the scale. So, the new
perimeter: 30 * 1/5
area: 50 * (1/5)^2
To find the perimeter and area of the quadrilateral PQRS after applying the scale factor of 1/5, you need to follow these steps:
1. Understand the scale factor: A scale factor of 1/5 means that every dimension of the original shape will be reduced by a factor of 1/5. In other words, the length, width, and all other measurements will be divided by 5.
2. Calculate the dimensions of the reduced quadrilateral: Start by dividing the perimeter by the scale factor (1/5). Since the perimeter of the original shape is 30mm, dividing it by 1/5 gives us:
Perimeter of reduced shape = 30mm ÷ (1/5) = 30mm × 5 = 150mm
3. Calculate the area of the reduced quadrilateral: We know that the area of the original shape is 50mm^2. To find the area of the reduced shape, we need to square the scale factor first. So (1/5)^2 = 1/25. Now, multiply the area of the original shape by the squared scale factor:
Area of the reduced shape = 50mm^2 × (1/25) = 50mm^2 ÷ 25 = 2mm^2
4. Final results: After applying the scale factor of 1/5, the perimeter of the quadrilateral PQRS is 150mm, and the area is 2mm^2.