Find the Area of a Triangle Whose Sides Are 9 Cm, 12 Cm and 15 Cm ? - Mathematics

Advertisements
Advertisements

Find the area of a triangle whose sides are 9 cm, 12 cm and 15 cm ?

Advertisements

Solution

The triangle whose sides are a = 9cm, b = 12 cm and c = 15 cm
The area of a triangle `=sqrt(s(s-a)(s-b)(s-c))`

Here 1s = semi-perimeter of a triangle
`2s = a + b + c`

`s=(a+b+c)/2=(9+12+15)/2=(36)/2=18cm`

∴ area of a triangle= `sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(18(18-9)(18-12)(18-15))=sqrt(18(9)(6)(3))`

`=sqrt(18cm xx3cmxx54cm^2) =54cm^2`

  Is there an error in this question or solution?
Chapter 17: Heron’s Formula - Exercise 17.1 [Page 8]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.1 | Q 2 | Page 8

RELATED QUESTIONS

Find the values of k so that the area of the triangle with vertices (k + 1, 1), (4, -3) and (7, -k) is 6 sq. units.


Find the area of the triangle PQR with Q(3,2) and the mid-points of the sides through Q being (2,−1) and (1,2).


Find the area of a triangle whose vertices are A(3, 2), B (11, 8) and C(8, 12).


If D, E and F are the mid-points of sides BC, CA and AB respectively of a ∆ABC, then using coordinate geometry prove that Area of ∆DEF = `\frac { 1 }{ 4 } "(Area of ∆ABC)"`


In each of the following find the value of 'k', for which the points are collinear.

(7, -2), (5, 1), (3, -k


Find the area of a triangle with vertices at the point given in the following:

(2, 7), (1, 1), (10, 8)


Find the area of a triangle with vertices at the point given in the following:

(−2, −3), (3, 2), (−1, −8)


Show that points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.


Find values of k if area of triangle is 4 square units and vertices are (k, 0), (4, 0), (0, 2)


Find values of k if area of triangle is 4 square units and vertices are (−2, 0), (0, 4), (0, k)


Find equation of line joining (3, 1) and (9, 3) using determinant.


Find the area of the following triangle:


Find the area of the following triangle:


Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm ?


Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm ?


In a ΔABC, AB = 15 cm, BC = 13 cm and AC = 14 cm. Find the area of ΔABC and hence its altitude on AC ?


The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle ?


Find the area of the blades of thc magnetic compass shown in Fig.. 12.27. (Take √11 = 3.32).


Show that the points are the vertices of an isosceles right triangle.


For what value of k(k>0) is the area of the triangle with vertices (-2, 5), (k, -4) and (2k+1, 10) equal to 53 square units?


Find the value of x for which points A(x, 2), B(-3, -4) and C(7, -5) are collinear.


 Using determinants, find the values of k, if the area of triangle with vertices (–2, 0), (0, 4) and (0, k) is 4 square units. 


In ☐ ABCD, l(AB) = 13 cm, l(DC) = 9 cm, l(AD) = 8 cm, find the area of ☐ ABCD.


Using integration, find the area of the triangle whose vertices are (2, 3), (3, 5) and (4, 4).


Using integration, find the area of triangle ABC, whose vertices are A(2, 5), B(4, 7) and C(6, 2).


What is the area of a triangle with base 4.8 cm and height 3.6 cm?


Find BC, if the area of the triangle ABC is 36 cm2 and the height AD is 3 cm.


If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is 


The table given below contains some measures of the right angled triangle. Find the unknown values.

Base Height Area
20 cm 40 cm ?

The table given below contains some measures of the right angled triangle. Find the unknown values.

Base Height Area
5 feet ? 20 sq.feet

The table given below contains some measures of the right angled triangle. Find the unknown values.

Base Height Area
? 12 m 24 sq.m

A field is in the shape of a right angled triangle whose base is 25 m and height 20 m. Find the cost of levelling the field at the rate of ₹ 45 per sq.m2


Let ∆ = `|("A"x, x^2, 1),("B"y, y^2, 1),("C"z, z^2, 1)|`and ∆1 = `|("A", "B", "C"),(x, y, z),(zy, zx, xy)|`, then ______.


If A, B, C are the angles of a triangle, then ∆ = `|(sin^2"A", cot"A", 1),(sin^2"B", cot"B", 1),(sin^2"C", cot"C", 1)|` = ______.


If the co-ordinates of the vertices of an equilateral triangle with sides of length ‘a’ are (x1, y1), (x2, y2), (x3, y3), then `|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|^2 = (3"a"^4)/4`


Show that the ∆ABC is an isosceles triangle if the determinant

Δ = `[(1, 1, 1),(1 + cos"A", 1 + cos"B", 1 + cos"C"),(cos^2"A" + cos"A", cos^2"B" + cos"B", cos^2"C" + cos"C")]` = 0


The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq.units. The value of k will be ______.


If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.


Find the area of the triangle whose vertices are (-2, 6), (3, -6), and (1, 5).


Let `Delta = abs (("x", "y", "z"),("x"^2, "y"^2, "z"^2),("x"^3, "y"^3, "z"^3)),` then the value of `Delta` is ____________.


The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is ______.


The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is ______.


The area of a triangle with base 4 cm and height 6 cm is 24 cm2.


The area of ∆ABC is 8 cm2 in which AB = AC = 4 cm and ∠A = 90º.


The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.


A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.


The dimensions of a rectangle ABCD are 51 cm × 25 cm. A trapezium PQCD with its parallel sides QC and PD in the ratio 9:8, is cut off from the rectangle as shown in the figure. If the area of the trapezium PQCD is `5/6` h part of the area of the rectangle, find the lengths QC and PD.


Find the missing value:

Base Height Area of parallelogram
______ 15 cm 154.5 cm2

The area of a triangle with vertices A, B, C is given by ______. 


Ratio of areas of ∆MNO, ∆MOP and ∆MPQ in the given figure is ______.


Area of triangle PQR is 100 cm2 as shown in the below figure. If altitude QT is 10 cm, then its base PR is ______.


Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is ______.


Observe all the four triangles FAB, EAB, DAB and CAB as shown in the given figure. 

  1. All triangles have the same base and the same altitude.
  2. All triangles are congruent.
  3. All triangles are equal in area.
  4. All triangles may not have the same perimeter.

In the given figure, area of ΔPQR is 20 cm2 and area of ΔPQS is 44 cm2. Find the length RS, if PQ is perpendicular to QS and QR is 5 cm.


Let a vector `αhati + βhatj` be obtained by rotating the vector `sqrt(3)hati + hatj` by an angle 45° about the origin in counter-clockwise direction in the first quadrant. Then the area of triangle having vertices (α, β), (0, β) and (0, 0) is equal to ______.


Using determinants, find the area of ΔPQR with vertices P(3, 1), Q(9, 3) and R(5, 7). Also, find the equation of line PQ using determinants.


Find the missing value:

Base Height Area of Triangle
22 cm ______ 170.5 cm2

Share
Notifications



      Forgot password?
Use app×