1 Answer

Psyill · Answer 1 · 2020-12-13T12:25:55+0000

Answer:

L.A. = 157.5 in²

Explanation:

Lateral Area:

We have five congruent triangles with base = 7in and height h = 9in.

The formula of an area of a triangle:

A_triangle=(bh)/(2)

Substitute:

$A_\triangle=((7)(9))/(2)=(63)/(2)=31.5\ in^2$

The Lateral Area:

$L.A.=5A_\triangle\to L.A.=5\cdot31.5=157.5\ in^2$

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:

$B=(a^2)/(4)√(25+10\sqrt5)\approx1.72048a^2$

Substitute a = 7in:

$B\approx1.72048(7^2)=84.303552\ in^2\approx84.3\ in^2$

The Surface Area:

$S.A.=157.5+84.3=241.8\ in^2$