Question

Find the area of the image below: Figure QRSTU is shown. Q is at 3, 0. R is at negative 3, 0. S is at negative 3, 7. T is at 1, 11. U is at 5, 7.

A)59 square units
 B)65 square units
 C)72 square units
 D)83 square units

Answer 1

The correct answer is 65 square units!! :) 

Answer 2

The are of QRSTU is 65 square units

B is correct.

Explanation:

Please see the attachment for figure QRSTU

Q is at (3,0)

R is at (-3,0)

S is at (-3,7)

T is at (1,11)

U is at (5,7)

First we make three triangle. Join SQ and QT

We get three triangle

ΔSRQ, ΔSQT and ΔTQU

Area of triangle formula

`\text{Area of triangle}=(1)/(2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

`\text{Area of triangle SRQ}=(1)/(2)|-3(0-0)-3(0-7)+3(7-0)|=21\text{ square unit}`

`\text{Area of triangle SQT}=(1)/(2)|-3(0-11)+3(11-7)+1(7-0)|=26\text{ square unit}`

`\text{Area of triangle TQU}=(1)/(2)|1(0-7)-3(11-7)+5(0-11)|=18\text{ square unit}`

Area of QRSTU = ar(ΔSRQ) + ar(ΔSQT) + ar(ΔTQU)

Area of QRSTU = 21 + 26 + 18

= 65 square unit

Hence, The are of QRSTU is 65 square units