Answer:
L.A. = 157.5 in²
S.A. = 241.8 in²
Step-by-step explanation:
Lateral Area:
We have five congruent triangles with base = 7in and height h = 9in.
The formula of an area of a triangle:
[tex]A_triangle=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_\triangle=\dfrac{(7)(9)}{2}=\dfrac{63}{2}=31.5\ in^2[/tex]
The Lateral Area:
[tex]L.A.=5A_\triangle\to L.A.=5\cdot31.5=157.5\ in^2[/tex]
Surface Area:
S.A. = L.A. + B
L.A. - lateral area
B - area of a base
The base is the regular pentagon. The formula of an area:
[tex]B=\dfrac{a^2}{4}\sqrt{25+10\sqrt5}\approx1.72048a^2[/tex]
Substitute a = 7in:
[tex]B\approx1.72048(7^2)=84.303552\ in^2\approx84.3\ in^2[/tex]
The Surface Area:
[tex]S.A.=157.5+84.3=241.8\ in^2[/tex]
