There is something wrong with this problem. The area of the bigger triangle is 2 (.5 x 2 x 2) and the smaller one is .5 as u mentioned therefore the shaded area must be equal to 1.5 or 3/2 as thats the difference of the bigger triangle minus the smaller one. Can someone please explain why u chose the answer given?

Mariam, here's how I approach this problem.

The area of URST = area PST - area PRU, as you noted. To find area PST, we need to know what TS is. Since PS is 2, by Phytagorean theorem, PT^2 + TS^2 = PS^2. Since PT = TS (isosceles triangle), we can substitute PT with TS, hence 2 x TS^2 = 2^2 =4. TS = √2.

Now we can calculate the area of PST, i.e., 1/2 x √2 x √2 = 1.

Next, let's calculate the area of the smaller triangle PUR. It is also an isosceles, since it is congruent with PTS. Hence PU = QR = UR = 1. Area PUR = 1/2 x 1 x 1 = 1/2.

Hence, the area of URTS = area PST - area PUR = 1 - 1/2 = 1/2, which is E.

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If your interested in a logical approach used to verify and will at least show you there's nothing wrong with the problem :)

The square root of 2 is often used as an example of an irrational number therefore this root is commonly known, at least it's approximate of 1.4
Breaking down the shaded area will give us (1/2) for the rectangle and (1/2)bh = (1/2)*(1/2)*(2-1.4) = (1/4) * (3/5) = (3/20) now we add the rectangle (1/2) and get (3/20) + (10/20) = (13/20)

Now we use 'eye balling' going along the answers since (1/2) is the only one which comes close to our approx. of (13/20).

Niels

[EDIT]
Since my goal isn't to give you confusion but take it away:
The logical conclusion is also that UT must be less than (1/2)
You can verify PT with 2*sin(45 degrees) = +/- 1.4 = sqrt(2) which comes from the mnemonic SOH sin = opposite / hypotenuse

What's tha answer bra

I feel the answer to this question be 0.7 .....I have attached my workspace here..... I applied the formula of the area of trapezium......and UT comes out to be 0.4......ST =2.4 and UR= 1...... Then applying the formula......we get 0.2*3.4=0.68

I feel the answer to this question be 0.7 .....I have attached my workspace here..... I applied the formula of the area of trapezium......and UT comes out to be 0.4......ST =2.4 and UR= 1...... Then applying the formula......we get 0.2*3.4=0.68

I feel the answer to this question be 0.7 .....I have attached my workspace here..... I applied the formula of the area of trapezium......and UT comes out to be 0.4......ST =2.4 and UR= 1...... Then applying the formula......we get 0.2*3.4=0.68