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 $3$ $3$ , its base has sides of length $5$ $5$ , and its base has a corner with an angle of $\frac{π}{4}$ $pi/4$ . 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 $3$ $3$ , its base has sides of length $5$ $5$ , and its base has a corner with an angle of $\frac{π}{4}$ $pi/4$ . What is the pyramid's surface area?

1 Answer

Impact of this question

1321 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-04T02:43:29

$T S A$ $color(green)(T S A)$ $A_{T} = A_{L} + A_{R} = 74.4063$ $color(green)(A_T = A_L + A_R = 74.4063)$

Explanation:

enter image source here

Total Surface Area of the pyramid is sum of the areas of the rhombus base $(A_{R})$ $(A_R)$ and the four side triangles $(A_{L} = 4 \cdot A_{t})$ $(A_L= 4 * A_t)$
$A_{T} = A_{L} + A_{R} = 4 A_{t} + A_{R}$ $A_T = A_L + A_R = 4A_t + A_R$

$A_{R} = a \cdot a sin θ = 5 \cdot 5 sin (\frac{π}{4}) = 25 \sqrt{2} = 35.3553$ $A_R = a*asin theta = 5 * 5 sin (pi/4) = 25sqrt2 = 35.3553$ #

A_L = 4 A_t = 4 * (1/2) (a * l)# where l is the slant height of the triangle.

But $l = \sqrt{{(\frac{a}{2})}^{2} + h^{2}} = \sqrt{{(\frac{5}{2})}^{2} + 3^{2}} = 3.9051$ $l = sqrt((a/2)^2 + h^2) = sqrt((5/2)^2 + 3^2) = 3.9051$

$:. A_L = 4 * (1/2) * 5 * 3.9051 = 39.051$

$color(green)(T S A)$ $color(green)(A_T = A_L + A_R = 39.051 + 35.3553 = 74.4063)$

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 $3$ $3$ , its base has sides of length $5$ $5$ , and its base has a corner with an angle of $\frac{π}{4}$ $pi/4$ . 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 3 33 , its base has sides of length 5 55 , and its base has a corner with an angle of pi/4 π4 pi/4 . 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 $3$ $3$ , its base has sides of length $5$ $5$ , and its base has a corner with an angle of $\frac{π}{4}$ $pi/4$ . What is the pyramid's surface area?