Advertisements
Advertisements
Question
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°.
Advertisements
Solution
Given, AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°
BC = `sqrt("DC"^2 - "BD"^2)`
= `sqrt( 13^2 - 12^2 )`
= 5 cm
Hence, perimeter = 8 + 10 + 13 + 5 = 36 cm
Area of ΔABD, `sqrt("s"("s"-"a")("s"-"b")("s"-"c"))`
Here, s = `("a"+"b"+"c")/2`
= `(10+12+8)/2`
= `30/2`
= 15 cm
ΔABD = `sqrt( 15( 15 - 8 )( 15 - 10 )( 15 - 12 ))`
= `sqrt( 15 xx 7 xx 5 xx 3 )`
= `15sqrt7`
= 39.7
Area of ΔBDC,
ΔBDC = `1/2` × 12 × 5
= 30
Now,
Area of ABCD = area of ΔABD + area of ΔBDC
= 39.7 + 30
= 69.7 sq.cm
APPEARS IN
RELATED QUESTIONS
ABC is a triangle in which AB = AC = 4 cm and ∠A = 90°. Calculate:
(i) The area of ΔABC,
(ii) The length of the perpendicular from A to BC.
The sides of a triangular field are in the ratio 5: 3: 4 and its perimeter is 180 m. Find:
- its area.
- the altitude of the triangle corresponding to its largest side.
- the cost of leveling the field at the rate of Rs. 10 per square meter.
Find the area of a triangle, whose sides are :
21 m, 28 m, and 35 m
Find the area of the right-angled triangle with a hypotenuse of 40 cm and one of the other two sides of 24 cm.
The perimeter of a triangle is 72cm and its sides are in the ratio 3:4:5. Find its area and the length of the altitude corresponding to the longest side.
The table given below contains some measures of the triangle. Find the unknown values.
| Side 1 | Side 2 | Side 3 | Perimeter |
| ? | 8 m | 3 m | 17 m |
The table given below contains some measures of the triangle. Find the unknown values.
| Side 1 | Side 2 | Side 3 | Perimeter |
| 11 feet | ? | 9 feet | 28 feet |
From one vertex of an equilateral triangle with side 40 cm, an equilateral triangle with 6 cm side is removed. What is the perimeter of the remaining portion?
In the following figure, all triangles are equilateral and AB = 8 units. Other triangles have been formed by taking the mid points of the sides. What is the perimeter of the figure?
Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
