7. 15° D A M 10 ED = 7 m, AD = 10 m and angle ADE = 15°. M is the midpoint of AD. N is the point on ED such that MN is at right angles to ED. Farmer Brown believes that N is the midpoint of ED. a. Calculate the area of triangle EAD.

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The roof was built using metal supports. Each support is made from five lengths of metal AE, ED, AD, EM and MN, and the design is shown in the
following diagram.
diagram not to scale
A
15°
10
ED = 7 m, AD = 10 m and angle ADE = 15°.
M is the midpoint of AD.
N is the point on ED such that MN is at right angles to ED.
Farmer Brown believes that N is the midpoint of ED.
a. Calculate the area of triangle EAD.
b. Calculate the total volume of the barn.
c. Calculate the length of MN.
d. Calculate the lengtf of AE.
e. Show that Farmer Brown is incorrect.
f. Calculate the total length of metal required for one support.
Transcribed Image Text:The roof was built using metal supports. Each support is made from five lengths of metal AE, ED, AD, EM and MN, and the design is shown in the following diagram. diagram not to scale A 15° 10 ED = 7 m, AD = 10 m and angle ADE = 15°. M is the midpoint of AD. N is the point on ED such that MN is at right angles to ED. Farmer Brown believes that N is the midpoint of ED. a. Calculate the area of triangle EAD. b. Calculate the total volume of the barn. c. Calculate the length of MN. d. Calculate the lengtf of AE. e. Show that Farmer Brown is incorrect. f. Calculate the total length of metal required for one support.
Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cubold base and a triangular prism roof, as shown in the
diagram.
diagram not to scale
L.
15
D
IH
K
16
B
10
The cuboid has a width of 10 m, a length of 16 m and a height of 5 m.
The roof has two slopitg faces and two vertical and identical sides, ADE and GLF.
The face DEFL slopes at an angle of 15° to the horizontal and ED = 7 m.
The roof was built using metal supports. Each support is made from five lengths of metal AE, ED, AD, EM and MN, and the design is shown in the
"ollowing diagram.
diagram not to scale
Transcribed Image Text:Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cubold base and a triangular prism roof, as shown in the diagram. diagram not to scale L. 15 D IH K 16 B 10 The cuboid has a width of 10 m, a length of 16 m and a height of 5 m. The roof has two slopitg faces and two vertical and identical sides, ADE and GLF. The face DEFL slopes at an angle of 15° to the horizontal and ED = 7 m. The roof was built using metal supports. Each support is made from five lengths of metal AE, ED, AD, EM and MN, and the design is shown in the "ollowing diagram. diagram not to scale
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