In the parallelogram find: the value of x, total perimeter and area of DEIK?
1 Answer
Mar 11, 2017
Perimeter of
Area of
Explanation:
From the diagram:
#EI = 4 = FH#
FGH forms a right angle triangle:
#FH=4, GH=10#
By Pyrthagoroius:
# GH^2=FH^2+FG^2#
# :. 100=16+FG^2#
# :. FG^2 = 84#
# :. FG = 2sqrt(21)#
From the diagram:
# KJ=2x=FG #
# :. 2x= 2sqrt(21)#
# :. x= sqrt(21)#
To calculate the perimeter of
# P = DE+EI+IJ+JK+DK #
# \ \ \ = x+4+x+2x+10 #
# \ \ \ = 14+4x #
# \ \ \ = 14+4sqrt(21) #
# \ \ \ ~~ 32.33 #
To calculate the area of
# A = "Area rect DEIJ" + "Area"triangle DJK #
# \ \ \ = DE*EI + 1/2(KJ)(DJ) #
# \ \ \ = x*4 + 1/2(2x)(4) #
# \ \ \ = 4x + 8x #
# \ \ \ = 12x #
# \ \ \ = 12sqrt(21) #
# \ \ \ ~~ 54.99 #
