Find surface area of a square pyramid with an area of 0.5cm and a length of 0.8cm. Round to the tenth and use proper units.
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base can be found by squaring the length of one side of the base. In this case, the base is a square, so the length of one side is 0.8 cm. Therefore, the area of the base is (0.8 cm)^2 = 0.64 cm^2.
Each of the four triangular faces of a square pyramid is an isosceles right triangle. To find the area of one of these triangles, we need to find the length of one of the legs and then use the formula for the area of a triangle: (0.5)(base)(height).
Let's start by finding the length of one of the legs. We can use the Pythagorean theorem: (leg)^2 + (leg)^2 = (hypotenuse)^2. Since the hypotenuse is the length of one side of the base (0.8 cm), we have (leg)^2 + (leg)^2 = (0.8 cm)^2. Solving for leg, we get leg ≈ 0.5657 cm.
Now we can find the area of one of the triangles: (0.5)(0.8 cm)(0.5657 cm) ≈ 0.2263 cm^2.
Since there are four triangular faces, the total area of the triangular faces is 4 times the area of one triangle: 4(0.2263 cm^2) = 0.9052 cm^2.
Finally, we can find the total surface area by adding the area of the base and the area of the triangular faces: 0.64 cm^2 + 0.9052 cm^2 = 1.5452 cm^2.
Rounded to the nearest tenth, the surface area of the square pyramid is 1.5 cm^2.