Question

What is a surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm round your answer to the nearest hundredth

Answer 1

To find the surface area of a square pyramid, we need to calculate the areas of its different faces.

The base of the pyramid is a square, so the area of the base is simply the side length squared. In this case, the base edge is 1.5 cm, so the area of the base is 1.5 cm * 1.5 cm = 2.25 cm².

The slant height is the height of each triangular face. Since all four triangular faces of the pyramid are congruent, we only need to calculate the area of one triangular face and then multiply it by four to get the total surface area.

The formula to calculate the area of a triangle is: (1/2) * base * height.

In this case, the base of the triangular face is the same as the base edge of the pyramid, which is 1.5 cm.

To find the height, we can use the Pythagorean theorem. The height, hypotenuse, and one of the sides of the triangular face form a right triangle.

Let's call the height of the triangular face "h." We can set up the following equation using the Pythagorean theorem:
h² + (0.5*base)² = slant height²
h² + (0.5*1.5)² = 4²
h² + 0.75² = 16
h² + 0.5625 = 16
h² = 16 - 0.5625
h² = 15.4375
h ≈ √15.4375 ≈ 3.93 cm (rounded to the nearest hundredth).

Now we can calculate the area of one triangular face:
(1/2) * base * height
= (1/2) * 1.5 cm * 3.93 cm
≈ 2.955 cm² (rounded to the nearest hundredth).

Since there are four triangular faces, we multiply the area of one face by four:
4 * 2.955 cm² = 11.82 cm².

Finally, we add the area of the base and the areas of the four triangular faces to find the total surface area of the pyramid:
2.25 cm² + 11.82 cm² = 14.07 cm² (rounded to the nearest hundredth).

Therefore, the surface area of the square pyramid is approximately 14.07 cm².