The diagram shows a logo. ABE and DCE are congruent triangles.
BCE is a sector of a circle, centre E.
Show that the area of the logo is 460 cm?
to 2 significant figures.
B В.
C
+
105°
E
27 cm
14 cm
32°
A
D

Step-by-step explanation:

From the picture attached,

Area of ΔECD =    

                       =

From ΔEFD,

sin(32°) =

sin(32°) =

EF = 14 × sin(32°)

    = 7.42 cm

By cosine rule,

EC² = DE² + CD² - 2(DE)(CD)cos(32°)

EC² = 14² + 27² - 2(14)(27)cos(32°)

EC² = 196 + 729 - 641.12

EC² = 283.88

EC = 16.85 cm

Area of ΔECD = Area of ΔAEB =

                                                   = 100.17

Area of ΔECD + Area of ΔAEB = 2(100.17)

                                                   = 200.34 cm²

Area of sector BEC =

Here, θ = central angle of the sector

Area of sector BEC =

                                =

                                = 260.16 cm²

Area of the logo = Area of triangles AEB + Area of triangle ECD + Area of sector BEC

= 200.34 + 260.16

= 460.50

≈ 460 cm²

c

step-by-step explanation: