Rectangular base pyramid

Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters.

Correct result:

S =  11.281 m2

Solution:

h=2.5 m a=2.8 m b=1.4 m  h1=h2+(b/2)2=2.52+(1.4/2)2≐2.5962 m h2=h2+(a/2)2=2.52+(2.8/2)2≐2.8653 m  S1=a⋅ h12=2.8⋅ 2.59622≐3.6346 m2 S2=b⋅ h22=1.4⋅ 2.86532≐2.0057 m2  S=2⋅ S1+2⋅ S2=2⋅ 3.6346+2⋅ 2.0057=11.281 m2h=2.5 \ \text{m} \ \\ a=2.8 \ \text{m} \ \\ b=1.4 \ \text{m} \ \\ \ \\ h_{1}=\sqrt{ h^2 +(b/2)^2 }=\sqrt{ 2.5^2 +(1.4/2)^2 } \doteq 2.5962 \ \text{m} \ \\ h_{2}=\sqrt{ h^2 +(a/2)^2 }=\sqrt{ 2.5^2 +(2.8/2)^2 } \doteq 2.8653 \ \text{m} \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ h_{1} }{ 2 }=\dfrac{ 2.8 \cdot \ 2.5962 }{ 2 } \doteq 3.6346 \ \text{m}^2 \ \\ S_{2}=\dfrac{ b \cdot \ h_{2} }{ 2 }=\dfrac{ 1.4 \cdot \ 2.8653 }{ 2 } \doteq 2.0057 \ \text{m}^2 \ \\ \ \\ S=2 \cdot \ S_{1}+2 \cdot \ S_{2}=2 \cdot \ 3.6346+2 \cdot \ 2.0057=11.281 \ \text{m}^2

Try another example


We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
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   video2

Next similar math problems:

  • Quadrilateral pyramid
    jehlan_4b_obdelnik Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
  • The Scout Tent
    jehlan_4b_obdelnik_2 The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high of pyramid roof?
  • Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  • Sum of squares
    pytagorean The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
  • Broken tree
    broken_tree The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
  • Pyramid four sides
    jehlan_4b_obdelnik_1 In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
  • Isosceles trapezoid
    lichobeznik_mo_z8_5 What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
  • Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • Roof of the church
    cone_church The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof?
  • Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  • The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  • A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  • Sailing
    ship_2 Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then When she docked and reached the fishing grounds she launched