Answer:
Step-by-step explanation:
we know that
The surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three triangular lateral faces
step 1
Find the area of the triangular base
we know that
The triangular base is an equilateral triangle
so
The area applying the law of sines is equal to
step 2
Find the area of its three triangular lateral faces
![A=3[\frac{1}{2}bh]](https://tex.z-dn.net/?f=A%3D3%5B%5Cfrac%7B1%7D%7B2%7Dbh%5D)
we have
Find the height of triangles
Applying the Pythagorean Theorem
solve for h
substitute
![A=3[\frac{1}{2}(14)\sqrt{51}]](https://tex.z-dn.net/?f=A%3D3%5B%5Cfrac%7B1%7D%7B2%7D%2814%29%5Csqrt%7B51%7D%5D)
step 3
Find the surface area
Adds the areas
Round to the nearest tenth
Answer:
Simplify the expression.
Exact Form:
2560/3
Decimal Form:
853.¯3
Mixed Number Form:
853 1/3
Step-by-step explanation:
The place value of the 2 in 6'025 is 20
The ladder must be 9.4 ft to reach the top of the building
Here, we want to get the length of the ladder that will reach the top of the building
Firstly, we need a diagrammatic representation
We have this as;
As we can see, we have a right triangle with the hypotenuse being the length of the ladder
We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Thus, we have;
![\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%3D5%5E2%2B8%5E2%20%5C%5C%20x%5E2%3D%5Ctext%7B%2025%20%2B%2064%7D%20%5C%5C%20x%5E2%5Ctext%7B%20%3D%2089%7D%20%5C%5C%20x%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B89%7D%20%5C%5C%20x%5Ctext%7B%20%3D%209.4%20ft%7D%20%5Cend%7Bgathered%7D)
Answer:
117.3
Step-by-step explanation:
7*4=117.29=117.3
