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].
The Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
A polyhedron that has a polygonal base and triangles for sides, is a pyramid.
The lateral area of the pyramid is equal to the area of its three triangular lateral faces is;
[tex]\rm Lateral \ Area=3 \times \dfrac{1}{2}\times b \times k\\\\ Lateral \ Area=3 \times \dfrac{1}{2}\times 10 \times 8\\\\ Lateral \ Area=120[/tex]
The surface area of the pyramid is;
[tex]\rm Surface \ area=\dfrac{1}{2}bh + Lateral \ area\\\\Surface \ area=\dfrac{1}{2}\times 10 \times 8.66 +120\\\\Surface \ area=43.3+120\\\\Surface \ area=163.3 \ cm^3[/tex]
Hence, the Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
To know more about the pyramid click the link given below.
https://brainly.com/question/1318557
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