Surface of pyramid

In a regular quadrilateral pyramid, the height of the sidewall is equal to the length of the edge of the base. The content of the sidewall is 32 cm2. What is the surface of the pyramid?

Correct result:

S =  160 cm2

Solution:

S2=32 cm2 S2=a h2 a=h S2=a2/2 a=2 S2=2 32=8 cm S1=a2=82=64 cm2  S=4 S2+S1 S=5 S2=5 32=160 cm2S_{2}=32 \ \text{cm}^2 \ \\ S_{2}=\dfrac{ a \cdot \ h }{ 2 } \ \\ a=h \ \\ S_{2}=a^2/2 \ \\ a=\sqrt{ 2 \cdot \ S_{2} }=\sqrt{ 2 \cdot \ 32 }=8 \ \text{cm} \ \\ S_{1}=a^2=8^2=64 \ \text{cm}^2 \ \\ \ \\ S=4 \cdot \ S_{2} + S_{1} \ \\ S=5 \cdot \ S_{2}=5 \cdot \ 32=160 \ \text{cm}^2



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Surface area 6
    prism3s Find the surface area of a prism whose bases are right triangles with sides of length 3, 4, and 5 inches and a height of 8 inches. Include a sketch
  • Greenhouse
    foliovnik Garden plastic greenhouse is shaped half cylinder with a diameter of 6 m and base length 20 m. At least how many m2 of plastic is need to its cover?
  • Pipe
    1pipes How long is the pipe with an outside diameter of 1.44 m if his coloring consumed 44 kg of color. 1 kg of color coverage is 9 m2.
  • Kitchen
    valcek_na_cesto Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Triangle ABC
    rozbor_triangle Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction
  • Garden
    map_6 The garden around the new majer is divided as follows: 35% vegetable, 30% fruit orchards, 10% flowers and the remaining 120 m2 are lawns. What is the total area of the garden?
  • Gloves
    rukavice I have a box with two hundred pieces of gloves in total, split into ten parcels of twenty pieces, and I sell three parcels. What percent of the total amount I sold?
  • New refrigerator
    lednice New refrigerator sells for 1024 USD, Monday will be 25% discount. How much USD will save, and what will be the price?
  • Percents - easy
    percents_5 How many percent is 432 out of 434?
  • MO 2016 Numerical axis
    osa Cat's school use a special numerical axis. The distance between the numbers 1 and 2 is 1 cm, the distance between the numbers 2 and 3 is 3 cm, between the numbers 3 and 4 is 5 cm and so on, the distance between the next pair of natural numbers is always i
  • Unknown number
    nums Identify unknown number which 1/5 is 40 greater than one tenth of that number.
  • The percentages in practice
    plodina If every tenth apple on the tree is rotten it can be expressed by percentages: 10% of the apples on the tree is rotten. Tell percent using the following information: a. in June rained 6 days b, increase worker pay 500 euros to 50 euros c, grabbed 21 fr
  • Base, percents, value
    percent_1 Base is 344084 which is 100 %. How many percent is 384177?
  • Inequation
    inequalities Solve the inequation: 5k - (7k - 1)≤ 2/5 . (5-k)-2
  • Class
    children_2 In a class are 32 pupils. Of these are 8 boys. What percentage of girls are in the class?
  • TVs
    tv Production of television sets increased from 3,500 units to 4,200 units. Calculate the percentage of production increase.