Find the area and the perimeter of quadrilateral ABCD, given below; if, AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.

Given: AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90° In Δ BCD, By using the Pythagoras theorem, Base 2 \+ Height 2 = Hypotenuse 2 ⇒ BC 2 \+ 12 2 = 13 2 ⇒ BC 2 \+ 144 = 169 ⇒ BC 2 = 169 \- 144 ⇒ BC 2 = 25 ⇒ BC = ⇒ BC = 5 cm Area of Δ BCD = x base x height = x 12 x 5 cm 2 = x 60 cm 2 = 30 cm 2 For Δ ABD, Let AD = a = 10 cm, BD = b = 12 cm and AB = c = 8 cm. ∵ Area of triangle = = cm 2 = cm 2 = cm 2 = 39.7 cm 2 Area of quadrilateral ABCD = Area of Δ ABD + Area of Δ BCD = 39.5 + 30 cm 2 = 69.5 cm 2 Perimeter of quadrilateral ABCD = Sum of all sides of quadrilateral = AB \+ BC \+ CD \+ DA = 8 \+ 10 \+ 13 \+ 5 = 36 cm Hence, the area of quadrilateral is 69.7 cm 2 and the perimeter is 36 cm.

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

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The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

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The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

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The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :
(i) its area.
(ii) altitude of the triangle corresponding to its largest side.
(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

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Mathematics

Find the area and the perimeter of quadrilateral ABCD, given below; if, AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.

Mensuration

Related Questions

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :
(i) its area.
(ii) altitude of the triangle corresponding to its largest side.
(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

Mathematics

Find the area and the perimeter of quadrilateral ABCD, given below; if, AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.

Mensuration

Related Questions

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m2 is ₹ 49,572; find its base and height.

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :(i) its area.(ii) altitude of the triangle corresponding to its largest side.(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

The sides of a triangular field are in the ratio 5 : 3 : 4 and its perimeter is 180 m. Find :
(i) its area.
(ii) altitude of the triangle corresponding to its largest side.
(iii) the cost of levelling the field at the rate of ₹ 10 per square metre.