**Triangle worksheet solution2 :**

Here we are going to see solution for each problems of the topic area of triangle worksheet.

(2) Vertices of the triangle taken in order and their areas are given below. In each of the following find the value of a.

(i) (0, 0), (4, a) and (6, 4) and its area is 17 sq.units

**Solution :**

Area of the triangle = 17 square units

17 = (1/2) [ (0 + 16 + 0) – (0 + 6 a + 0) ]

(1/2)(16 – 6 a) = 17

(1/2) **⋅** 2 (8 - 3a) = 17

8 – 3 a = 17 ==> -3a = 17 – 8

-3a = 9

a = 9/(-3)

a = -3

Hence, the required vertices is (4, -3)

(ii) (a, a) , (4 , 5) and ( 6 , -1) and its area is 9 sq.units

**Solution :**

Area of the triangle = 9 square units

9 = (1/2) [(5a - 4 + 6a) – (4a + 30 - a)]

(1/2)[ (11a – 4) – ( 3a+30) ] = 9

(1/2) [11a – 4 – 3a - 30 ] = 9

(1/2) [8 a – 34 ] = 9

8 a – 34 = 18 ==> 8 a = 18 + 34

8 a = 52 ==> a = 58/8 ==> a = 13/2

Hence, the required vertex is (13/2 , 13/2)

(iii) (a, -3),(3, a) and (-1, 5) and its area is 12 sq.units

**Solution :**

Area of the triangle = 12 square units

12 = (1/2)[ (a² + 15 + 3) – (-9 - a + 5a) ]

(1/2)[ (a² + 18 ) – (-9 + 4a) ] = 12

[a² + 18 + 9 - 4a ] = 12 x 2

a² - 4a + 27 = 24

a² - 4a + 27 - 24 = 0

a² - 4a + 3 = 0

(a - 1) (a - 3) = 0

a = 1 , 3

- Section formula
- Area of quadrilateral
- Centroid
- Midpoint
- Distance between two points
- Distance between two points worksheet
- Slope of the line
- Equation of the line
- Equation of line using two points worksheet
- Equation of the line using point and slope worksheets
- Point of intersection of two lines
- concurrency of straight line
- Circumcentre of a triangle
- Orthocentre of a triangle
- Incentre of a triangle
- Locus
- Perpendicular distance
- Angle between two straight lines
- Equation of a circle
- With center and radius
- With endpoints of a diameter
- Equation of a circle passing though three points
- Length of the tangent to a circle
- Equation of the tangent to a circle
- Family of circles
- Orthogonal circles

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