Question

A kite is in the shape of a square with diagonal 40cm and an isosceles triangle of base 6cm and sides 4cm. The area of the figure (in sq.cm) is:​

Answer 1

Step-by-step explanation:

Let a point be 'O' dividing UV in half.

After dividing, OU = OV = 6cm/2 = 3cm

Since ∆ROU is a right-angled triangle, we will apply the Pythagoras Theorem to find RO, So according to the Pythagoras Theorem :

: OR² + OU² = RU²

: OR² + 3² = 4²

: OR² + 9 = 16

: OR² = 7

: OR = √7

Hence, OR = √7cm

Area of the isosceles triangle RUV = ((6 × √7)/2) cm²

= 3√7 cm²

With the help of Pythagoras Theorem, we will also find each side of the Square :

*(Let each side of the square be 'x' cm)

: x² + x² = 40²

: 2x² = 1600

: x² = 800

: x = 20√2

Hence Each side of the square is 20√2 cm

Area of the square : (20√2 × 20√2) cm²

: 800cm²

Area of the total figure = 800cm² + 3√7 cm²

= (800 + 3√7) cm²

Hence, the answer is (800 + 3√7) cm²

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