please can some one answer this question important?

Question

A garden has the shape ,where ABDE is a rectangle and such that AE = 40m, AB = 60m while BC = DC = 32 m.?
shape is like:
a******b
*************c
e******d
(i) Calculate the cosine of the angle at C. Use your calculator to find the measure of
this angle to the nearest degree
(ii) Calculate the area of the triangle BCD in m2 correct to two decimal places.
Show your work
(iii) Calculate the area, in m2, of the whole garden (to 2 decimal places).
Show your work
(iv) A fence is to be built around the outside perimeter of the garden. If the cost of the
fence is 2.75 £ per running meter then, calculate the total cost of the fence, to 2
decimal places

Answer 1

Base of triangle is BD is 40
Sides are BC and DC which are 32
Let F be midpoint of BD. We now have a right angle triangle
BCF with BF 20 and BC 32.

By Pythagoras
BC^2 = BF^2 + CF^2
32^2 = 20^2 + CF^2
1024 = 400 + CF^2
624 = CF^2
CF = sqrt(624) = 4 sqrt(39)

Now
cosine( = 4 sqrt(39) / 32
= 0.7806

Area of triangle BCD is 1/2 (CF) * (BD) or
1/2 * 4 sqrt(39) * 40
= 499.60 m^2

The area of teh whole garden is area of ABDE + area of BCD

Area of ABDE is AE * AB or 40 * 60 = 2400.00 m^2
Area of ABCDE is 2400.00 + 499.60 or 2899.60 m^2

Cost of fence will be length of fence * 2.75
Length of fence is AB + BC + CD + DE + AE or
60 + 32 + 32 + 60 + 40 = 224 m

Cost will be 224 * 2.75 = 616.00 £

Answer 2

BCD is an isosceles triangle whose sides you know. Therefore you can calculate its area with formula #4 from:

http://www.btinternet.com/~se16/hgb/triangle.htm

Since this is also equal to (1/2) x Base x Height, you can compute the distance from C to the line BD. This gives you the sine and cosine of half the angle at C.

To get the cosine of the full angle, use the trig identity:
cos 2@ = cos^2 @ - sin^2 @

http://en.wikipedia.org/wiki/List_of_trigonometric_identities

The rest is easy.