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lara [203]
3 years ago
7

The pyramid shown has a square base that is 12 centimeters on each side. The slant height is 18 centimeters. What is the surface

area of the pyramid?
Mathematics
2 answers:
Sav [38]3 years ago
8 0
<span>The <u>correct answer</u> is:

576 sq. cm.

Explanation:

The surface area of a figure is the sum of the areas of the faces of the figure.

The slant height goes from the apex of the pyramid along a face and is perpendicular to the base at the bottom of that face. This gives us 2 measurements of each triangular face of the pyramid: the height (the slant height of the pyramid is the height of the triangular face), 18 cm, and the base <span>of the triangular face, 12 cm.

The formula for the area of a triangle is A = 1/2bh; using our measurements we have:
A = 1/2(12)(18) = 108 sq. cm.

There are 4 triangular faces on a square pyramid, and each will have an area of 108 sq. cm.; this gives us:
4(108) = 432 sq. cm.

The area of the base is given by length times width, or 12*12 = 144 sq. cm.

This gives us a total surface area of 432+144=576 sq. cm.</span></span>
blagie [28]3 years ago
3 0

Answer:

The total surface area of the pyramid = 576 cm²        

Step-by-step explanation:

The base of the pyramid is square with the side length of 12 cm

So, Area of the base of pyramid = (side)²

                                                      = 12 × 12

                                                     = 144 cm²

Now, to find the area of the triangle : length = 12 cm and height = 18 cm

Area of the triangle = 0.5 × length × height

                                 = 0.5 × 12 × 18

                                 = 108 cm²

So, Area of 4 triangles in the pyramid = 4 × 108

                                                               = 432 cm²

Hence, The total surface area of the pyramid = 144 + 432

                                                                               = 576 cm²

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