ABC is an isosceles triangle with AB = AC = 13 cm and base BC = 10cm. A square is inscribed in the triangle. Find the area of square and shaded region.

See First Draw a Triangle Having sides AB= 10 cm,BC=10 cm and AC=13 cm.Now Draw a Square in it.The Area of Triangle will be 1/2*base * height= 1/2* 10* √69 = 41.5.Let the side of the square be x.So Now The Area of the whole square will be equal to Area of the Upper small portion of Triangle+ Below Two Small side triangles.Just apply the condition and find the side x of the triangleYou will get the area of square as 1.05 cmand Area of Triangle is 41.5For area of shaded region = Area of Triangle - Area of Square= 41.5- 1.05= 40.4 cm.

AB= 13 cm*** (Mistyped) There is no option to add image else I might add the image for better understanding.I`m sure you will get the values by this.If still you stuck,feel free to ask here :)Thanks for using AskIITians!