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CUBE and CUBOID

CUBE and CUBOID. To calculate the sum of edges, length of face/plane diagonal, and diagonal, also area of diagonal plane. Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com. Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com. CUBE. H. G. F.

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CUBE and CUBOID

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  1. CUBE and CUBOID To calculate the sum of edges, length of face/plane diagonal, and diagonal, also area of diagonal plane Created by CepAndiAlimSubarkah for mathlabsky.wordpress.com Created by CepAndiAlimSubarkah for mathlabsky.wordpress.com

  2. CUBE H G F E = r cm D C = r cm A B r cm EXAMPLE 1 = EXAMPLE 2

  3. Face/Plane Diagonal H G Look at ∆BAE, ∠A is right angle. F E + + r cm D C r cm A B r cm

  4. Diagonal H G Look at ∆CAE, ∠A is right angle. E F + + r cm D C r cm A B r cm

  5. Diagonal Plane H G Look at rectangle ABGH F E r cm D C r cm A B r cm

  6. EXAMPLE 1 Given a cube with measure of edge is 4 cm. calculate The sum of edges c. The length of diagonal The length of face diagonal d. The area of diagonal plane The answer: d. The area of diagonal plane → = = cm2 a. The sum of edges →12 x r = 12 x 4cm = 48 cm b. The length of face diagonal → r= 42 = = 32cm c. The length of diagonal → r= 43 = = 48cm

  7. EXAMPLE 2 Given a cube with measure of face diagonal is cm. calculate The sum of edges c. The area of diagonal plane The length of diagonal The answer: a. The sum of edges →12 x r = 12 x 6cm = 72 cm b. The length of diagonal → r= 63 = = 108cm e. The area of diagonal plane → = = cm2

  8. CUBOID G H F E h cm D C w cm A B l cm Example 1 Example 2

  9. Face/Plane Diagonal G H Look at ∆CBF, ∠B is right angle. F E + h cm + D C w cm A B l cm + Look at ∆ABC, ∠B is right angle. +

  10. Diagonal G H F E Look at ∆CAE, ∠A is right angle. h cm D C + w cm A B + l cm

  11. EXAMPLE 1 H G Given a cuboid. Calculate The sum of edges Face diagonal on based The diagonal E F 9 cm D C 6 cm The answer : A B 10 cm The sum of edges : 4 (l + w + h) : 4 (10 + 6 + 9) : 4 (25) : 100 cm b. Length of : : : :

  12. H G E The face diagonal on based : : : : F 9 cm D C 6 cm A B 10 cm d. The diagonal : : : :

  13. EXAMPLE 2 Sebuahbalokmemilikiukuranrusuk alas 8 cm x 10cm. Jikapanjangseluruhrusukbalokadalah 92cm, makapanjang diagonal ruangbalokadalah … Jawab PanjangrusukSeluruh = 92 4 (p + l+ t) = 92 4 (8 + 10+ t) = 92 4 (18 + t) = 92 18 + t = 92 : 4 = 23 t = 23 – 18 = 5 Panjang diagonal ruang : : : : : cm

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