give me your closest estimate
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.(1 point)
To find the surface area of a square pyramid, we need to calculate the area of the base and the lateral faces.
The area of the base can be found by squaring the length of one side of the base:
Area of base = (1.5 cm)^2 = 2.25 cm^2
Next, we need to find the area of the four lateral faces. Each lateral face is a triangle, and the area of a triangle can be found using the formula:
Area of triangle = (1/2) * base * height
In this case, the base of each lateral face is the length of one side of the base (1.5 cm), and the height can be found using the Pythagorean theorem:
Height^2 = (slant height)^2 - (base/2)^2
Height^2 = 4 cm^2 - (1.5 cm/2)^2
Height^2 = 4 cm^2 - (0.75 cm)^2
Height^2 = 4 cm^2 - 0.5625 cm^2
Height^2 = 3.4375 cm^2
Height ≈ √3.4375 cm ≈ 1.85 cm (rounded to nearest hundredth)
Now we can calculate the area of each lateral face:
Area of one lateral face = (1/2) * base * height
Area of one lateral face = (1/2) * 1.5 cm * 1.85 cm ≈ 1.39 cm^2
Since there are four lateral faces, the total area of the lateral faces is:
Total area of lateral faces = 4 * 1.39 cm^2 = 5.56 cm^2
Finally, we can find the surface area by adding the area of the base and the area of the lateral faces:
Surface area = Area of base + Total area of lateral faces
Surface area = 2.25 cm^2 + 5.56 cm^2 ≈ 7.81 cm^2 (rounded to nearest hundredth)
So, the estimated surface area of the square pyramid is 7.81 cm^2.