Triangle-triangle-Triangle

Alternatively you could do a quick count and see that 24 triangles could fit inside of this quadrilateral. Each triangle has an area of 1/2 bh = 1/2 * 2 * 2 = 2.

24 * 2 = 48.

if a triangle is isosceles it means that it is a right triangle so we can use Pythagoras' Theorem ie, abc triangle then a^2 + b^2 = c^2 √4+4=√8 so 3 hypotenuse = √8+√8+√8=3√8=the length rectangle 2 hypotenuse= √8+√8= 2√8=breadth of the rectangle therefore area = lxb=3√8x2√8=48 sq units

solve the lenght of the hypotenuse, x3 then x2 then multiply the 2 products, you have the area then, so simple

To find the hypotenuse of the right isosceles triangle, Use $\sec 45^\circ or \csc 45^\circ$ of 2= $\square{2} \times 2$ = $2 \square{2}$

OK so there is 3 hypotenuse on the length and 2 hypotenuse on the width, so use large of a square formula:

$L=l \times w=(2 \square{2} \times 3) \times (2 \square{2} \times 2)=(2 \square{2})^2 \times 6=8 \times 6=48$

Here , (2^2+2^2)^1/2=8^1/2 Then , Length = 3 * (8^1/2) ; Width = 2 * (8^1/2) ; So , area = Length * Width , = 48 ;

you can use the 45-45-90 rule and notice the length of the hypotenuse of each triangle is 2^(3/2) the first dimension has 3 of them, giving you a total of 3 2^(3/2) and the other dimension has 2 of them giving you 2 2^(3/2) taking the product gives you 6 2^(3/2+3/2)=6 8=48

(2sqrt2x3) x (2sqrt2x2)=48

If the short sides of an isosceles triangle are 1cm, the long side is √2 therefore the long side of the rectangle must be 6 x √2 and the short side 4 x √2. You can also write 6 x √2 x 4 x √2 as 6 x 4 x √2 x √2. Obviously √2 x √2 = 2 so this simplifies it to 6 x 4 x 2. The answer then is 6 x 4 x 2 = 48.

One side is 6sqrt2. Other side is 4sqrt2. So the product is 6* 4* 2=48. Area=48.

Area=24*2=48

Consider the triangles as isosceles right triangle then third side becomes 2 root 2 .length of the quad becomes 3 2 root 2 and breadth becomes 4 2 root 2..multiply both to get 48

this is not a square as the title says

The area = (3 x hypotenuse) x (2x hypotenuse) of the triangles. Now, each hypotenuse= sqrt(2^2 + 2^2)= sqrt(8). So, toatal area = 3 x sqrt(8) x 2 x sqrt(8) = 48.

One side is six times sqrt 2. The other side is 4 times sqrt 2. The product is 6 x 4 x 2 equals 48.

It has 24 symmetric Isosceles triangles each has an area of 2 units.

So 24*2 = 48

2 triangles will make an area of 1/2 * (2+2) * 2, that's 4 cm^2 - we call it m. Each row - represented by the upper triangles - can be filled with 4 m's, and we have a total of 3 rows. So the total area is m * 4 * 3 = 4 * 4 * 3 = 48 cm^2.

Answered it based on symmetry..

you can use the 45-45-90 rule and notice the length of the hypotenuse of each triangle is 2^(3/2) the first dimension has 3 of them, giving you a total of 3 2^(3/2) and the other dimension has 2 of them giving you 2 2^(3/2) taking the product gives you 6 2^(3/2+3/2)=6 8=48

we first find hypotenuse of issocelus triangle as: h^2= 2^2+2^2 h= 8^1/2 hence from figure the breath of quadrilateral = 3 8^1/2 and lenght =2 8^1/2

 so AREA of quad= length  *  breath
                                      =2*8^1/2  * 3*8^1/2
                                       =6 * 8
                                       = 48

since the triangle is isosceles and right-triangle, and therefore the hypotenuse is 2sqrt2. the Length=L of the quad. is 3 2sqrt2=6sqrt2 the Width=W of quad, is 2 sqrt2=4sqrt2 Area of the quad. is: A=L W =6sqrt2 4sqr2 =24*2 = 48

Length=3 sqrt(2^2+2^2)=3sqrt8 Breadth=2 sqrt(2^2+2^2)=2sqrt8 Area=L*B=48

Ok so here how it's done. First we know that the triangles are isosceles, it means that the two legs are equal. Being right triangles, we can solve for the hypotenuse then after which getting the length of the rectangle by multiplying the hypotenuse, which is 2.83 (rounded off; originally 2(square root of 2), by 3 and multiplying it again by 2 to get the width. Then multiply the length and the width to get its area. :)

After drawing all the remaining isosceles triangles, it can be seen that the isosceles triangles are 45 by 45 by 90 degree right triangle. The area of one triangle is 2. There are 24 triangles. Therefore, the area is 2x24 = 48.

( 3x2/cos 45)x (5x2/cos 45) I might of wrote it wrong. But isosceles right triangles are 45 deg ends and the hypotenuse is 2/cos45 deg. A = LxW.. I'm no expert. I'm just trying to relearn math

rectangle is 3 times the base of one triangle and twice the base of the same triangle essentially 3x * 2x, this means the answer wold logically be a multiple of 6. ((3*2)x)so the answer is not 8. it cannot be 12 because that would means the triangles are equilateral, which they arent. that leaves 24 or 48. it could not be 24, the base of the triangles would need to be as long as both other sides combined, this could never be correct, the triangle would be a straight line. therefore the answer is 48 :)

Here we can just find the areas of each triangle as we know that all the triangles are isosceles so we can find the area of each triangle by using 1/2 X b X h and then the area of all the 7 triangle comes out to be 28 and it is obvious that the area of quadrilateral will be greater then area of triangles and in the options only one option i.e 48 is available . So the answer will be 48

45,45,90 degree rule

To get the area of the rectangle, you need base along with height. You use the pythagorean theorem to get the unknown length of the triangle, which would be \sqrt{8}. 3 of the sides are the length of the rectangle, and 2 of them are the height. Length \times width is would be 3\sqrt{8} \times \ 2\sqrt{8}. 2 \times 3 is six. \sqrt{8} \times \sqrt{8} is equal to 8, and lastly, 6 \times 8 is equal to 48.

it also can be solved by pythagorus theoram that in isoselles triangle two sides are equal ie 2cm so by pythagorus hypoteneous^2=perpendiculer^2+base^2 ie sqrt of 2^2+2^2=2aqrt2 so one side of quadilateral=3times 2sqrt2=6aqrt2 and other side same as=4sqrt2 so area =4sqrt2*6sqrt2 =48.

The two triangles on the upper right of the quadrilateral make one larger triangle which has sides measuring 2-4-2 with height = 2 (the base is the side measuring 4). A = 1/2(bh) = 1/2(4)(2) = 4. Two of this triangle with A = 4 makes a square with A = 8. And six of this square can be contained in the given quadrilateral. So, 6*8 = 48.

Because it's right angles, all the triangles given are 45-45-90. Using this info, you can calculate that the hypotenuse is 2sqrt(2). 4sqrt(2) x 6sqrt(2) = 48, easy.

in this Quadrilateral 24 triangle are drawn and then find the area of one triangle that is 1/2 * 2 *2 = 2 sq.cm. and then multiply the area of one triangle by 24. so the correct answer is 2 * 24 = 48 sq.cm.

I got the answer right but that wasn't correct. No where is it mentioned that the quadrilateral has perpendicular sides or isosceles triangles are right angled. There is no other way to find the answer than assume that it is so. Hence, I would say, the question is incomplete.

triangle is right angled isosceles....so the side along the boundary of quadrilateral is 2* (2^0.5)......along the length are 3 triangles and along the breadth are 2 triangles.....

all the triangles are right angled triangle so by using Pythagoras theory 2^2+2^2=2√2.As there are 3triangles in length we get3x2√2=6√2 & in breadth we have 2 triangles so 2x2√2=4√2 .area of rectangle =lxb=48