Question

The dimensions of a cuboid with vertices A, B, C, D, E, F, G and H are as shown in Fig. 16.4.

(i) Which edges are of length 4 cm? Which edges are of length 5 cm?
(ii) Which faces have area equal to 20 cm²?
(iii) Which faces have the largest area? What is this largest ares?
(iv) Which faces have a diagonal equal to 5 cm?
(v) What is the area of the base of this cuboid?
(vi) Do all the lateral faces have the same area?

Answer 1

(i) The edges of 4 cm length are AD, EH, BC, and FG.
​The edges of 5 cm length are AB, EF, CD and GH.
(ii) The faces having dimensions of 5 cm x 4 cm would have an area of 20 cm². And such faces are ABCD and EFGH.
(iii) ABCD and EFGH have the largest area of 20 cm²​.
(There are three pairs of opposite faces of equal area. The area of opposite faces are: 3 x 4 cm², 4 x 5 cm², and 3 x 5 cm².
And among these, 4 x 5 cm² is the largest.

(iv) The faces having sides of 3 cm and 4 cm respectively would have the diagonal of 5 cm. (As hypotenuse of a right- angles triangle is: 3² + 4² = 5²). Therefore, the faces ADHE and BCGF have the diagonal of 5 cm.
(v) The base has q dimension of 4 cm x 5 cm, so area of abase is: 4 x 5 = 20 cm².

(vi) No, all lateral faces do not have the same area. The two lateral faces have an area of 3 x 5 = 15 cm² and rest of the two lateral faces have an area of 3 x 4 = 12 cm².