# 13.2.3 The Pythagoras’ Theorem, PT3 Focus Practice

   
     
      
Question 6: In the diagram shows two right-angled triangles. Calculate the perimeter of the whole diagram.
      
      

    Solution:
      
In ∆ ABC,
      
AC= 62 + 82
      
 = 36 + 64
      
 = 100
      
AC = √100
      
= 10 cm
      
AD = 5 cm
      
      

    In ∆ EDC,
      
EC= 122 + 52
      
 = 144 + 25
      
 = 169
      
EC = √169
      
= 13 cm
      
      

    Perimeter of the whole diagram
      
= AB + BC + CE + DE + AD
      
= 6 + 8 + 13 + 12 + 5
      
= 44 cm
  
  
 

  
      
      
Question 7:
      
In the diagram, ABCD is a trapezium and AED is a right-angled triangle. Calculate the area, in cm2, of the shaded region.
      
      

    Solution:
      
AD= 52 + 122
      
 = 25 + 144
      
 = 169
      
AD = √169
      
= 13 cm
      
Area of trapezium ABDC
      
= ½ (13 + 15) × 9
      
= 126 cm2
      
      

    Area of triangle AED
      
= ½ × 5 × 12
      
= 30 cm2
      
      

    Area of the shaded region
      
= 126 – 30
      
= 96 cm2