Method 1 : guess and check :

Isosceles △ means they have two equal sides. Since both triangles are right-angled and bigger △'s sides are 2cm longer than the smaller △'s

Try :

½ × 10cm × 10cm - ½ × 8cm × 8cm

= ½ × (10 × 10 - 8 × 8)cm²

= ½ × (100 - 64)cm²

= ½ × 36cm²

= 18cm²


Or

½ × 10cm × 10cm - ½ × 8cm × 8cm

= ½ × 100cm² - ½ × 64cm²
= 50cm² - 32cm²
= 18cm²



The longer side is 10cm so AB is 8cm

Method 2 :

The shaded area can be divided into many smaller right-angled isosceles triangles.

Area of one such triangle
= ½ × 2cm × 2cm
= ½ × 4cm²
= 2cm²

Number of such triangles that can be cut from the shaded area

= 18cm² ÷ 2cm²
= 9

When arranged, number of triangles that line up to be as long as AB = 4

Length of AB = 4 × 2cm = 8cm

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