jeremyroyal06
Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

What Is The Lateral Surface Area Of The Square Pyramid Represented By This Net class=

Sagot :

semsee45

Answer:

340 ft²

Step-by-step 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

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]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.