Question

Olivia is cutting a 1 \dfrac12 \text{ m}1
2
1
​
m1, start fraction, 1, divided by, 2, end fraction, start text, space, m, end text by \dfrac34\text{ m}
4
3
​
mstart fraction, 3, divided by, 4, end fraction, start text, space, m, end text piece of rectangular paper into two pieces along its diagonal.
Find the area of each of the pieces.

​

Answer 1

Given:

Dimension of the rectangular paper:

length = $1\frac{1}{2}\:m$ = $\frac{3}{2}$

breadth = $\frac{3}{4}\:m$

Olivia cuts the paper into two pieces along its diagonal

To find:

The area of each of the pieces

Solution:

Olivia will cut the rectangular paper along its diagonal into two pieces.

After cutting she will get two triangular pieces, which will be congruent to each other by SAS congruency. [every angle of a rectangle = 90°, opposite facing sides are equal and a common side (diagonal)]

∴ Area of each of the triangular pieces will be given by,

= ½ × Area of the rectangular paper

= ½ × [length × breadth]

= ½ × [$\frac{3}{2} \:\times\:\frac{3}{4}$]

= ½ × $\frac{9}{8}$

= $\bold{\frac{9}{16} \:m}$

Thus, the area of each of the pieces is $\bold{\underline{\frac{9}{16} \:m}}$.

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Answer 2

Answer: the area of pieces is 9/16m^2

Step-by-step explanation:

lets DRAW A DIAGRAM TO YOU PIECE OF PAPER.

each of pieces is a tringle with the same base and height.

area of the triangle = 1/2 x 1 and 1/2 x 3/4  

                                 = 9/16 m^2