GB-36-02-001 · Similar areas

Two similar shapes have corresponding lengths in the ratio 5 : 16. The smaller has area 400 cm². Find the area of the larger.

Similar Shapes: L.A.V Table (Area) Booklet p. 41

Method

1) Put corresponding measurements in an L.A.V table (or L.L for two lengths)

2) Length factor r, area factor r², volume factor r³

3) Multiply from small to large; divide in reverse

Worked Example (GB-36-02-001)

Dimension	Small	Scale factor: small → large	Large
L	5	$\frac{16}{5}$	16
A	400	$(\frac{16}{5})^{2}$	$400\times(\frac{16}{5})^{2}=4096$

Ans = 4096 cm²