Question

AB is a line of symmetry of this arrow shape. A)Calculate The Perimeter of the shape.

B) The Value of H
C) The area of the shape

Answer 1

A)58cm

B)
`h=4√(5)cm`

C)125.55square cm

Explanation:

AB is a line is symmetry

Total length of left half part=12cm+9cm+3cm+5cm

Total length of left half part=29 cm

Length of left half part=Length of right half part

Therefore, length of right half part=29 cm

A) Perimeter of the shape=29cm+29cm=58cm

B)

Pythagoras theorem

`(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2`

Hypotenuse=12 cm

Base=5+3=8cm

In triangle ADC

Now, using Pythagoras theorem

`(12)^2=8^2+h^2`

`144=64+h^2`

`h^2=144-64=80`

`h=√(80)=4√(5)cm`

C)

Area of shape=Area of triangle+ area of rectangle

Area of shape=
`(1)/(2)* b* h+l* b`

Where l=9cm

breadth=3+3=6cm

h=
`4\sqt{5}cm`

base=2(5)+3(2)=16cm

Area of shape=
`(1)/(2)** 16* 4√(5)+9* 6`

Area of shape=125.55 square cm