Q11 of 99 Page 267

Skakil draws an equilateral triangle PQR. I draw three perpendiculars from appoint inside of that equilateral triangle on three sides, of which lengths are 10 cm, 12 cm and 8 cm. Let us write by calculating the area of triangle.

Given, PQR is an equilateral triangle



Let PQ = QR= PR = x cm and AC = 10cm, AB = 12 cm and AD = 8cm


Area of the equilateral triangle =


⇒ area of equilateral triangle PQR =


Here,


Area of triangle PQR = area of triangle PAR


+ area of triangle RAQ


+ area of triangle PAQ


= (∵ area of triangle= 1/2 ×base× height)


In this case the perpendicular is height of the that particular triangle


= 4x + 6x + 5x


According to the given condition


15x =


= x


Now


Area of equilateral triangle PQR =


= cm2


= cm2


= 300√3cm2


More from this chapter

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9

The ratio of the length of sides of a triangular park of our village is 2:3:4; perimeter of park is 216 meter.

(i) Let us write by calculating the area of the park.


(ii) Let us write by calculating how long is to be walked from opposite vertex of longest side to that side straightly.

 10

The length of three sides of a triangular filed of village of Paholampur are 26 meter, 28 meter and 30 meter.

(i) Let us write by calculating what will be the cost of planting grass in the triangular field at the rate of Rs. 5 per sq. meter.


(ii) Let us write by calculating how much cost will be for fencing around three sides at the rate Rs. 18 per meter leaving a space 5 meter for constructing entrance gate of that triangular field.

 12

The length of each equal side of an isosceles triangle is 20 m and the angle included between them is 45°. Let us write by calculating the area of triangle.

 13

The length of each equal side of an isosceles triangle is 20 cm, and the angle included between them is 30°. Let us write by calculating the area of triangle.