1. Find the number of triangles in the given figure
(A) 28
(B) 32
(C) 36
(D) 40
Answer: Option C
Explanation:The simplest triangles are AML, LRK, KWD, DWJ, JXI, IYC, CYH, HTG, GOB, BOF, FNE and EMA i.e. 12 in number.
The triangles composed of two components each are AEL, KDJ, HIC and FBG i.e. 4 in number.
The triangles composed of three components each are APF, EQB, BQH, GVC, CVJ, IUD, DUL and KPA i.e. 8 in number.
The triangles composed of six components each are ASB, BSG, CSD, DSA, AKF, EBH, GGJ and IDL i.e. 8 in number.
The triangles composed of twelve components each are ADB, ABC, BCD and CDA i.e. 4 in number.
Total number of triangles in the figure = 12 + 4 + 8 + 8 + 4 = 36.
2. Count the number of cubes in the given figure.
(A) 130
(B) 132
(C) 138
(D) 140
Answer: Option D
Explanation:In the figure, there are
5 columns containing 4 cubes each
33 columns containing 3 cubes each;
9 columns containing 2 cubes each and 3 columns containing 1 cube each.
∴ Total Number of cubes = ( 5 x 4) + (33 x 3) + (9 x 2) + (3 x 1) = 20 + 99 + 18 + 3 = 140