Chapter 6.3, Problem 40PPE

To determine

To calculate: Area of each square and triangle.

Answer to Problem 40PPE

Area of square, $81$ cm² and area of triangle, $15$ cm²

Explanation of Solution

Given information: Total area of figure A is $141$ cm². The total area of B is $192$ cm².

Calculation:

Let’s assume area of square is $x$ cm²and area of triangle is $y$ cm² Now, figure A consists of four triangles and one square with total area $141$ cm²,

  $\therefore 4y+x=141$......(i)

Now, figure B consists of two square and two triangles with total area $192$ cm²,

  $\therefore 2y+2x=192$......(ii)

Let’s multiply equation two with two and subtract it from equation one,

  $4y+x=141$

  $\_\underset{\_}{4y+4x=384}$

  $-3x=-243$

  $\therefore x=81$

Let’s put the value of $x$ in first equation,

Now, put value of $y$ in third equation,

  $\therefore y=15$