Answer:
3.9 cm²
Explanation:
You want the area of shape C if the ratios of perimeters of similar shapes C, D, E are C:D = 1:3 and D:E = 2:5, and the total area is 260 cm².
Perimeter ratio
The perimeters of the figures can be combined in one ratio by doubling the C:D ratio and multiplying the D:E ratio by 3
C:D = 1:3 = 2:6
D:E = 2:5 = 6:15
Then ...
C : D : E = 2 : 6 : 15 . . . . . . . perimeter ratios
Area ratio
The ratios of areas are the square of the ratios of perimeters. The area ratios are ...
C : D : E = 2² : 6² : 15² = 4 : 36 : 225 . . . . . . area ratios
The fraction of the total area that figure C has is ...
4/(4+36+225) = 4/265
Then the area of C is ...
(4/265)·(260 cm²) ≈ 3.9 cm²
The area of C is about 3.9 cm².
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