It is known that the side lengths of two bottom surfaces of a regular triangular pyramid are 30cm and 20cm respectively, and the side area is equal to the sum of the two bottom areas

It is known that the side lengths of two bottom surfaces of a regular triangular pyramid are 30cm and 20cm respectively, and the side area is equal to the sum of the two bottom areas


The area of the two bottoms is 225 √ 3 and 100 √ 3 respectively,
The side is isosceles trapezoid, the top and bottom are 20 and 30 respectively
(20+30)*h/2=225√3+100√3
The height is 13 √ 3cm
The volume of the pyramid is
1/3*13√3*[225√3+100√3+√(225√3*100√3)]=6175cm³



The length of the top and bottom sides of a square pyramid is 4cm and 10cm respectively, and the height is 4cm


According to the meaning of the title, if the oblique height h ′ = 32 + 42 = 5, the side area of the regular pyramid is 12 × 4 × (4 + 10) × 5 = 140, and the volume is 13 × 4 (42 + 102 + 42 × 102) × 4 = 208



The oblique height of a pyramid is 12cm, the side edge length is 13cm, and the side area is 720cm2. Find the side length of its upper and lower bottom surfaces


10cm and 20cm
According to the meaning of the title, the four sides are isosceles trapezoid, with waist length of 13cm and trapezoid height of 12cm
If the side length of the upper bottom is a, the side length of the lower bottom can be expressed as a + 10
A = 10 (CM) is obtained when the side area of four surfaces is 4 × (a + A + 10) × 12 / 2 = 720