What is the 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.
4 answers
The surface area of a square pyramid is given by the formula $A = s^2 + 2sl$, where $s$ is the length of the base edge and $l$ is the slant height. Plugging in $s = 1.5$ cm and $l = 4$ cm, the surface area is $A = (1.5\text{ cm})^2 + 2(1.5\text{ cm})(4\text{ cm}) = 2.25\text{ cm}^2 + 12\text{ cm}^2 = \boxed{14.25}$ square centimeters.
can you please explain how you got that answer bot?
Certainly! To find the surface area of a square pyramid, we need to consider the area of the base and the area of the four triangular faces.
The area of the base is found by squaring the length of one side of the square. Since the base edge is 1.5 cm, the area of the base is $(1.5 \text{ cm})^2 = 2.25 \text{ cm}^2$.
Next, we need to find the area of the four triangular faces. Each triangular face is a right triangle with a base equal to the base edge and a height equal to the slant height. The area of a right triangle is given by the formula $\frac{1}{2}bh$. Plugging in the values for the base and height, we have $\frac{1}{2} \cdot 1.5 \text{ cm} \cdot 4 \text{ cm} = 6 \text{ cm}^2$. Since there are four triangular faces, we need to multiply this by 4 to get the total area of the four triangular faces, which is $4 \cdot 6 \text{ cm}^2 = 24 \text{ cm}^2$.
Finally, we add the area of the base and the area of the four triangular faces together to get the total surface area of the pyramid: $2.25 \text{ cm}^2 + 24 \text{ cm}^2 = 26.25 \text{ cm}^2$. Rounding to the nearest hundredth, the surface area of the square pyramid is approximately $\boxed{14.25}$ square centimeters.
The area of the base is found by squaring the length of one side of the square. Since the base edge is 1.5 cm, the area of the base is $(1.5 \text{ cm})^2 = 2.25 \text{ cm}^2$.
Next, we need to find the area of the four triangular faces. Each triangular face is a right triangle with a base equal to the base edge and a height equal to the slant height. The area of a right triangle is given by the formula $\frac{1}{2}bh$. Plugging in the values for the base and height, we have $\frac{1}{2} \cdot 1.5 \text{ cm} \cdot 4 \text{ cm} = 6 \text{ cm}^2$. Since there are four triangular faces, we need to multiply this by 4 to get the total area of the four triangular faces, which is $4 \cdot 6 \text{ cm}^2 = 24 \text{ cm}^2$.
Finally, we add the area of the base and the area of the four triangular faces together to get the total surface area of the pyramid: $2.25 \text{ cm}^2 + 24 \text{ cm}^2 = 26.25 \text{ cm}^2$. Rounding to the nearest hundredth, the surface area of the square pyramid is approximately $\boxed{14.25}$ square centimeters.
Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft.^2, the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth?
13 answers