Answer:
340 ft²
Step-by-step explanation:
The surface area of a shape is basically the area of its faces.
[tex]\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}[/tex]
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.
[tex]\rightarrow \text{Area of triangle} = \dfrac{12 \times 10}{2}[/tex]
Now, let's find the area of the triangle by simplifying the RHS.
[tex]\rightarrow \text{Area of triangle} = 6 \times 10[/tex]
[tex]\rightarrow \text{Area of triangle} = 60 \ \text{ft}^{2}[/tex]
Since there are four triangles, we need to further multiply the area of the triangle by 4 to find the area of four triangles.
[tex]\rightarrow \text{Area of four triangles} = 4(60)[/tex]
[tex]\rightarrow \text{Area of four triangles} = 240 \ \text{ft}^{2}[/tex]
2. Now, let's find the area of the square. To find the area of the square, we need to square the side length.
[tex]\rightarrow \text{Side length} = 10 \ \text{ft}[/tex]
[tex]\rightarrow \text{Area of square} = 10^{2}[/tex]
[tex]\rightarrow \text{Area of square} = 100 \ \text{ft}^{2}[/tex]
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.
[tex]\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}[/tex]
[tex]\rightarrow \text{Surface area of pyramid: 240 + 100}[/tex]
[tex]\rightarrow \text{Surface area of pyramid: 340 \text{ft}}^{2} }[/tex]
