The base edge of the regular triangular pyramid is b=10 cm and altitude of the base hb ≈ 8.66 cm. The slant height of the pyramid is k=8 cm. Find: Lateral area and Surface area of the pyramid

Answer:Step-by-step explanation:It is given that the base edge of the regular triangular pyramid is b=10 cm and altitude of the base h =8.66 cm. The slant height of the pyramid is k=8 cm. Now, the lateral surface area of the pyramid is given as:[tex]LSA={\frac{3}{2}}(b)(k)[/tex]Substituting the given values, we have[tex]LSA=\frac{3}{2}(10)(8)[/tex][tex]LSA=120cm^2[/tex]Thus, the Lateral surface area of the pyramid is [tex]120cm^2[/tex].Now, the surface area is given as:[tex]SA=\frac{1}{2}bh+LSA[/tex][tex]SA=\frac{1}{2}bh+120[/tex][tex]SA=\frac{1}{2}(10)(8.66)+120[/tex][tex]SA=43.3+120[/tex][tex]SA=163.3cm^2[/tex]Thus, the surface area of the pyramid will be [tex]163.3cm^2[/tex].