The pre-image that has undergone dilation with a scale of 2 / 5 has a surface area of the image after the dilation as [tex]206\frac{2}{25}[/tex] m²
How to find the surface area after dilation?
The surface area of the image after dilation is calculated as follows;
a₂ = a₁ k²
where
a₁ = surface area of the pre-image
a₂ = surface area of the image
k = represents the scale factor = [tex]\frac{2}{5}[/tex]
Therefore,
a₁ = (7 × 20) + 2(1 /2 × 24 × 7) + (20 × 25) + (20 × 24)
a₁ = 140 + 168 + 500 + 480
a₁ = 1288 m²
Therefore,
a₂ = 1288 × (2 / 5)²
a₂ = 1288 × 4 / 25
a₂ = 5152 / 25
a₂ = [tex]206\frac{2}{25}[/tex] m²
learn more on surface area here:https://brainly.com/question/27053295
