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# What is the area of RST ?

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Math Expert
Joined: 02 Sep 2009
Posts: 46302
What is the area of RST ? [#permalink]

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31 May 2018, 12:01
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:23) correct 10% (01:32) wrong based on 73 sessions

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What is the area of RST ?

A. 6

B. $$2 \sqrt{13}$$

C. 10

D. 12

E. 24

Attachment:

RST.jpg [ 16.31 KiB | Viewed 618 times ]

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Joined: 31 Jan 2018
Posts: 72
Re: What is the area of RST ? [#permalink]

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31 May 2018, 13:14
Bunuel wrote:

What is the area of RST ?

A. 6

B. $$2 \sqrt{13}$$

C. 10

D. 12

E. 24

Attachment:
RST.jpg

Coordinate of R (6,0), S(6,4) and O(0,0)

Length of RO = sqrt[(0-6)^2 + (0-0)^2] = 6
Length of SR = sqrt[(6-6)^2 + (4-0)^2] = 4

RO = ST

Therefore the area of triangle RST = 1/2 * 6 * 4 = 12
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Joined: 04 Jan 2015
Posts: 1596
Re: What is the area of RST ? [#permalink]

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01 Jun 2018, 03:13

Solution

To find:
• The area of the triangle RST

Approach and Working:
• As SR is perpendicular to x axis and ST is perpendicular to y axis, the coordinates of point S represents the distance of the point S from x axis and y axis respectively
o Distance of S from x axis = 6 unit
o Distance of S from y axis = 4 unit
• RST is a right-angled triangle, therefore the area of RST = ½ * SR * ST = ½* 4 * 6 = 12 sq. unit
Hence, the correct answer is option D.

[In other way, the line RT is the diagonal of the rectangle ORST. Hence, area of triangle RST = ½ of area of rectangle ORST = ½ * 6 * 4 = 12]
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Re: What is the area of RST ? [#permalink]

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01 Jun 2018, 03:44
1
Bunuel wrote:

What is the area of RST ?

A. 6

B. $$2 \sqrt{13}$$

C. 10

D. 12

E. 24

Attachment:
RST.jpg

Area of the triangle = (1/2) Base * Height
Here base of RST = ST = 6 (x-Co-ordinate of Point S)
Here Height of RST = RS = 4 (Y-Co-ordinate of Point S)

Hence, Area= (1/2)*4*6 = 12

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

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01 Jun 2018, 03:58
OA: D
Area of rectangle 0RST =$$6*4 =24$$

Quote:
Each diagonal divides the rectangle into two congruent right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the rectangle

Area of $$\triangle$$ RST=$$\frac{1}{2}*24=12$$
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Re: What is the area of RST ? [#permalink]

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03 Jun 2018, 18:23
Bunuel wrote:

What is the area of RST ?

A. 6

B. $$2 \sqrt{13}$$

C. 10

D. 12

E. 24

Attachment:
RST.jpg

We see that leg TS = 6 and leg SR = 4. Thus, the area is 6 x 4 x 1/2 = 12.

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

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04 Jun 2018, 02:22
Bunuel wrote:

What is the area of RST ?

A. 6

B. $$2 \sqrt{13}$$

C. 10

D. 12

E. 24

Attachment:
RST.jpg

Let 'O' be the origin of the given xy-plane.

so, ORST is an rectangle with length,OR=TS=6 unit and breadth,OT=SR=4 unit

Now, required area of triangle RST=$$\frac{1}{2}$$* Area of rectangle ORST=$$\frac{1}{2}$$*TS*SR=$$\frac{1}{2}$$*6*4=12

Hence, Option(D) is correct.
Re: What is the area of RST ?   [#permalink] 04 Jun 2018, 02:22
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