Answer:
Area of rectangle PLUM = 75.00 square units
Step-by-step explanation:
Since diagonal of rectangle divides the rectangle into two equal triangles,
Therefore, area of the rectangle PLUM = 2× area of triangle PLM
By the mean proportional theorem,
In ΔPLM,
AP² = AM × AL
6² = AM × 8
AM =
AM = 4.5 units
Area of PLM = 
= 
= 
= 12.5 × 3
= 37.5 units²
Now area of rectangle PLUM = 2×37.5 = 75 units²
Therefore, area of the rectangle is 75.00 square units.
Answer:
x=6, AB=61, BC=61, AC=122
Step-by-step explanation:

9514 1404 393
Answer:
168 cubic inches
Step-by-step explanation:
The formula for the volume of a pyramid is ...
V = (1/3)Bh
where B is the area of the base, and h is the height.
The base is a rectangle, whose are is given by the formula ...
A = LW
A = (8 in)(7 in) = 56 in²
Then the pyramid volume is ...
V = (1/3)(56 in²)(9 in) = 168 in³
The volume of the pyramid is 168 cubic inches.
Answer: 480 units^2
IN DEPTH EXPLANATION TO HELP YOU FOR FUTURE PROBLEMS:
Front:
b*h/2 = sa
12*5/2 = 30
Front = 30 units^2
Back:
b*h/2 = sa
12*5/2 = 30
Back = 30 units^2
Right:
w*l = sa
14*13 = 182 units^2
Right: 182 units*2
(figures out the length by using
pythagorean theorem)
Left:
w*l = sa
5*14 = 70 units^2
Left: 70 units^2
Bottom:
w*l = sa
12*14 = 168 units^2
ADD ALL THE UNITS:
168 + 70 + 182 + 30 + 30 = 480
<u>To prove the trigonometric equation:</u>


We know that
, substitute this in place of 1.

Multiply each term of the first term with each term of the 2nd term.

Group like terms together.



= LHS
RHS = LHS

Hence proved.