A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #3 # and the pyramid's height is #7 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?
T S A = 38.5312
Area of parallelogram base
Area of
Area of
Lateral surface area =
Total surface area =Area of parallelogram base + Lateral surface area
By signing up, you agree to our Terms of Service and Privacy Policy
To find the surface area of the pyramid, we need to calculate the area of the base and the lateral area.

Area of the base: Since the base is a parallelogram, its area is given by the formula: ( \text{Area of parallelogram} = \text{base} \times \text{height} ). Given the base's sides are 2 and 3, the area of the base is ( 2 \times 3 = 6 ) square units.

Lateral area: The lateral area of a pyramid is given by the formula: ( \text{Lateral area} = \frac{1}{2} \times \text{perimeter of base} \times \text{slant height} ). To find the perimeter of the base, we add the lengths of the four sides: ( 2 + 3 + 2 + 3 = 10 ). Now, we need to find the slant height. We can use trigonometry with the given angle. The slant height (( l )) is given by ( l = \frac{\text{height}}{\sin(\text{angle})} ). Given the height is 7 and the angle is ( \frac{5\pi}{6} ), ( l = \frac{7}{\sin\left(\frac{5\pi}{6}\right)} ). Using trigonometric identities, we know ( \sin\left(\frac{5\pi}{6}\right) = \sin\left(\pi  \frac{\pi}{6}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} ). So, ( l = \frac{7}{\frac{1}{2}} = 14 ). Now, plug these values into the formula to find the lateral area: ( \text{Lateral area} = \frac{1}{2} \times 10 \times 14 = 70 ) square units.

Total surface area: The total surface area is the sum of the base area and the lateral area: ( \text{Total surface area} = \text{Base area} + \text{Lateral area} = 6 + 70 = 76 ) square units.
So, the surface area of the pyramid is ( 76 ) square units.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 A rectangle's length #y# is half the square of it's width #x#. The perimeter is 48m. What are the rectangle's dimensions?
 In isosceles triangle has congruent sides of 20 cm. The base is 10 cm. How do you find the height of the triangle?
 A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #12 # and the height of the cylinder is #24 #. If the volume of the solid is #42 pi#, what is the area of the base of the cylinder?
 Each side a cube is 18 meters long. What is the surface area of the cube?
 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 #5 #, its base has sides of length #2 #, and its base has a corner with an angle of # pi/3 #. What is the pyramid's surface area?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7