Question

Find the surface area of a square pyramid with side length 1 mi and slant height 3 mi

Answer 1

Answer:

20

Step-by-step explanation:

The answer is 20

+ 4(1/2⋅2 mi⋅4 mi) = 4

​

Four triangles: 4 (1/2 b * h)

Add them up= 20 mi  

Answer 2

Surface area of the square pyramid is 7 square mi .

What is a square pyramid ?

A square pyramid is a three-dimensional geometric figure which has a square base and four lateral faces, The lateral faces are triangular faces with a common vertex.

How to calculate the surface area of a square pyramid ?

Let us consider a square pyramid, whose side length is "a" and slant height is "h".

Then the area of the base, i.e. area of square shaped base = $a^{2}$ square unit and the area of each triangular face is ($\frac{1}{2}$×a×h) square unit .

So, the sum of areas of 4 triangular faces is 4×($\frac{1}{2}$×a×h)=2ah square unit .

∴ Surface area of a square pyramid = Area of base + Area of 4 side faces

                                                           = ($a^{2}$+2ah) square unit

Given that, Side length(a)=1 mi

& Slant height(h)=3 mi

∴ Surface area of the given square pyramid = $(1)^{2}$+(2×1×3) square mi

                                                                         = 1+6 square mi

                                                                         = 7 square mi

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