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Properties of Congruent and Similar Solids

What is the surface area of the smaller solid? The solids are similar.

base, 4 sides, 4 triangles

$\frac{15}{10} = \frac{12}{\mathrm{x}} \quad 15\mathrm{x}=120 \quad x=8\mathrm{in}$

$\frac{15\mathrm{x}}{15}=\frac{120}{15}$

$\mathrm{A=8in \cdot 10in} = 80in^2$

$\mathrm{4(80in)=320in^2}$

$\frac{15}{10}=\frac{16}{h} \quad 160=15h \quad h = 10.67\mathrm{in \quad or \quad} 10 \frac{2}{3}\mathrm{in}$

$\frac{160}{15}=\frac{15h}{15}$

$\mathrm{A=\dfrac{1}{2}bh}$
$\mathrm{A=\dfrac{1}{2}(10in)(19.67in)}$
$\mathrm{A=53.33in^2}$
$(53.33\mathrm{in}^2)(4)=213.33\mathrm{in}^2$
$\mathrm{A=(s)(s)=s^2}$
$\mathrm{A=(10)(10)=100}$
$\mathrm{S_{total}=A_{sides}+A_{triangles}+A_{base}}$
$\mathrm{=320in^2+213.33in^2+100in^2=633.33in^2}$