Question

Identify the lateral area and surface area of a regular triangular pyramid with base edge length 10 ft and slant
height 14 ft

Answer 1

Answer:

L = 315 cm2 ; S = 399.9 cm2

Step-by-step explanation:

Lateral area;

3 × (½)(14)(15)

315 cm²

Surface area:

315 + (½)(14)(14)sin(60)

399.8704896 cm²

Answer 2

    Lateral surface area of the regula triangular pyramid is 210 ft²

    Surface area of the regular triangular pyramid is 253.30 ft²

Lateral area and Surface area of a triangular pyramid:

•  Expression for the lateral area of a regular triangular pyramid is given by,

          Lateral surface area = 3(Area of one lateral triangular side)

•   Expression for the total surface area is given by,

          Surface area = Area of the triangular base + Lateral surface area

Given in the question,

•  Base with the edge length = 10 feet
•  Slant height = 14 ft

Lateral surface area = $3(\frac{1}{2})(\text{Base})(\text{Slant height})$

                                  = $\frac{3}{2}(10)(14)$

                                  = 210 ft²

Area of the regular triangular base = $\frac{\sqrt{3} }{4}(a)^2$

                                                          = $\frac{\sqrt{3} }{4}(10)^2$

                                                          = 25√3 ft²

                                                          = 43.30 ft²

Therefore, total surface area = 210 + 43.30

                                                 = 253.30 ft²

     Hence, lateral surface area of the regula triangular pyramid is 210 ft²

                   Surface area of the regular triangular pyramid is 253.30 ft²

Learn more aboiut the surface area and lateral surface area here,

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