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

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