Question

What is the lateral surface area of the square pyramid represented by this net?

Answer 1

340 ft²

Explanation:

The surface area of a shape is basically the area of its faces.

`\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}`

1. First, Let's find the area of the triangles. To find the area of a triangle, we need to multiply the height and the base and then divide the product by 2.

`\rightarrow \text{Area of triangle} = (12 * 10)/(2)`

Now, let's find the area of the triangle by simplifying the RHS.

`\rightarrow \text{Area of triangle} = 6 * 10`

`\rightarrow \text{Area of triangle} = 60 \ \text{ft}^(2)`

Since there are four triangles, we need to further multiply the area of the triangle by 4 to find the area of four triangles.

`\rightarrow \text{Area of four triangles} = 4(60)`

`\rightarrow \text{Area of four triangles} = 240 \ \text{ft}^(2)`

2. Now, let's find the area of the square. To find the area of the square, we need to square the side length.

`\rightarrow \text{Side length} = 10 \ \text{ft}`

`\rightarrow \text{Area of square} = 10^(2)`

`\rightarrow \text{Area of square} = 100 \ \text{ft}^(2)`

3. Lastly, let's find the surface area. To find the surface area of the figure, we need to sum up the area of the triangles and the area of the square.

`\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}`

`\rightarrow \text{Surface area of pyramid: 240 + 100}`

`\rightarrow \text{Surface area of pyramid: 340 \text{ft}}^(2) }`

Answer 2

340 ft²

Explanation:

From the diagram, we can see that the shape is made up of a square and 4 triangles. (We know it's a square as its width equals its length).

First, find the area of the square.

Area of a square = width x length = 10 x 10 = 100 ft²

All the triangles are the same, so we need to find the area of one of the triangles and multiply it by 4.

Area of a triangle = 1/2 x base x height = 1/2 x 10 x 12 = 60 ft²

So the total area of all 4 triangles = 4 x 60 = 240 ft²

Therefore the total surface area = 100 + 240 = 340 ft²