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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the lateral area for the regular pyramid.L. A. =Find the total area for the regular pyramid.T. A. =

Click An Item In The List Or Group Of Pictures At The Bottom Of The Problem And Holding The Button Down Drag It Into The Correct Position In The Answer Box Rele class=

Sagot :

Answer

LA = 4√10

TA = 4 + 4√10

Step-by-step explanation

To find the Lateral Area (LA) of the pyramid, first, we need to calculate its slant height (s).

Considering the right triangle formed inside the pyramid, we can apply the Pythagorean theorem to find the length of s, as follows:

[tex]\begin{gathered} s^2=3^2+1^2 \\ s^2=9+1 \\ s=\sqrt{10} \end{gathered}[/tex]

Now, we can calculate the lateral area as follows:

[tex]\begin{gathered} LA=\frac{1}{2}\times P\operatorname{\times}s \\ \text{ where P is the perimeter of the base of the pyramid. Substituting }P=4\times2\text{ and }s=\sqrt{10}: \\ LA=\frac{1}{2}\operatorname{\times}4\operatorname{\times}2\operatorname{\times}\sqrt{10} \\ LA=4\sqrt{10} \end{gathered}[/tex]

To find the total area (TA) of the pyramid, first, we need to calculate the area of its base (B). In this case, the base is a square, then its area is:

[tex]\begin{gathered} B=b^2\text{ \lparen where b is the length of each edge\rparen} \\ B=2^2 \\ B=4 \end{gathered}[/tex]

Finally, the total area is calculated as follows:

[tex]\begin{gathered} TA=B+LA \\ TA=4+4\sqrt{10} \end{gathered}[/tex]

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