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# What is the area of the figure above?

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
What is the area of the figure above?  [#permalink]

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17 Jan 2019, 23:35
1
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:52) correct 25% (01:04) wrong based on 36 sessions

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What is the area of the figure above?

A 18
B 24
C 26
D 32
E 40

Attachment:

2019-01-18_1033.png [ 4.02 KiB | Viewed 579 times ]

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Re: What is the area of the figure above?  [#permalink]

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18 Jan 2019, 04:46
Bunuel wrote:

What is the area of the figure above?

A 18
B 24
C 26
D 32
E 40

Attachment:
2019-01-18_1033.png

draw a line we get a triangle in 3:4:5
so width of rectangle = 4
area = 0.5 * 4*3 +5*4 = 26
IMO C
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Joined: 15 Feb 2018
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Re: What is the area of the figure above?  [#permalink]

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19 Jan 2019, 01:58
Area of a trapezoid is 0.5(height)(a+b) where a+b is the top and bottom of the trapezoid

The height in the figure is found using the pythagorean triple 3-4-5.
The base is 3 (8-5), hypotenuse 5, so height must be 4.

0.5(4)(5+8)=2·13=26
C
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Re: What is the area of the figure above?  [#permalink]

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19 Jan 2019, 02:46
Easy one ,Drop a line from <ABC to be perpendicular to line DC let’s name it E now since line DC is 8 then line EC is 3
Now we can recognize a Pythagorean triplet 3:4:5 or better still solve for line BE with pythagoras theory
Since the figure is a trapezoid as line AB || DC but different in length
We average line AB and DC and multiply by BE which becomes the height
Therefore 1/2(5+8)x 4=26

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Re: What is the area of the figure above?  [#permalink]

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22 Apr 2019, 23:04
What is the area of the figure above?

A 18
B 24
C 26
D 32
E 40

Since we need to find the area of the figure,
Break up the figure into a rectangle + a triangle.

Drop a perpendicular from point B onto line DC.
This perpendicular divides DC into two segments, i.e. 5 units + 3 units = 8 units
Take this 3 units as one side of the triangle and find out the other side using pythagorean theorem,
h2 = a2 + b2

Calculate area of rectangle + area of triangle = total area
i.e., (length*breadth) + (1/2 * base * height) = total area

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Re: What is the area of the figure above?   [#permalink] 22 Apr 2019, 23:04
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