A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is $6$ $6$ , its base's sides have lengths of $5$ $5$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . What is the pyramid's surface area?

Question

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is $6$ $6$ , its base's sides have lengths of $5$ $5$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . What is the pyramid's surface area?

1 Answer

Impact of this question

1443 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-18T03:23:25

Total surface area of the pyramid $= 70.4308$ $= 70.4308$

Explanation:

Side of Rhombus = 5
Vertical height = 6

Slant length of pyramid = sqrt(6^2 + (5/2)^2) = 6.5
Lateral surface area of pyramid = 4(1/2)5 * 6.5 = 65#

Now to find the base area
Let the diagonals be $d_{1} & d_{2}$ $d_1 & d_2$
$\frac{d_{1}}{2} = 5 \cdot sin (\frac{\frac{5 π}{8}}{2}) = 5 \cdot sin (\frac{5 π}{16}) = 0.9755$ $d_1 /2 = 5*sin (((5pi)/8)/2) = 5*sin ((5pi)/16) = 0.9755$
$d_{1} = 2 \cdot .9775 = 1.955$ $d_1 = 2*.9775 = 1.955$
$\frac{d_{2}}{2} = 5 \cdot cos (\frac{5 π}{16}) = 2.7779$ $d_2 / 2 = 5* cos((5pi)/16) = 2.7779$
$d_{2} = 2.7779 \cdot 2 = 5.5558$ $d_2 = 2.7779*2 = 5.5558$
Area of Rhombus = (d_1d_2)/2 =(1.9555.5558)/2=5.4308#

Total surface area $= 65 + 5.4308 = 70.4308$ $= 65 + 5.4308 = 70.4308$

Science

Math

Humanities

... and beyond

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is $6$ $6$ , its base's sides have lengths of $5$ $5$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . What is the pyramid's surface area?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is 6 66 , its base's sides have lengths of 5 55 , and its base has a corner with an angle of (5 pi)/8 5π8(5 pi)/8 . What is the pyramid's surface area?

1 Answer

Explanation:

Related questions

Impact of this question

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is $6$ $6$ , its base's sides have lengths of $5$ $5$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . What is the pyramid's surface area?