f.3 math 1question @10m

The top part consists of 4 isosceles triangles.
In each isosceles triangle, the height, one of the sides and half of the base form a right-angled triangle with the side as the hypotenuse.

By Pythagorean theorem, the height
= √[(16)² - (22/2)²] cm
= √ 135 cm
= 3√ 15 cm

Total area of the 4 isosceles triangles
= 4 x (22 x 3√15)/ 2 cm ²
= 132√ 15 cm ²

Area of the base
= ( 22 cm )²
= 484 cm ²

If the base the included, the surface area of the top part
= (484 + 132√15) cm²

If the base the excluded, the surface area of the top part
= 132√ 15 cm ²

1)要搵條正方形底的斜邊....即

12^2+12^2=斜邊^2(pyth. thm.)
斜邊=(√968)

2) 再將斜邊除2---------------->= (√968) /2

3)搵height
height^2+[(√968) /2]^2=16^2 (pyth. thm.)
height=√14

4)搵half of the length--------------->22/2=11cm'

5)搵slant
(√14)^2+11^2=slant ^2( pyth. thm.)
slant=√135

6)area of one side of triangle=[22(√135)]/2
=44√135