###### Advertisements

###### Advertisements

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

###### Advertisements

#### Solution

Area of the blades of magnetic compass = Area of ΔADB + Area of ΔCDB

Now, for area of ΔADB

Let, 2s = AD + DB + BA (Perimeter of ΔADB)

Semi perimeter (S)= `1/2(5+1+5)=11/2 cm`

By using heron’s formulae

Now, area of ΔADB `=sqrt(s(s-ad)(s-bd)(s-ba))`

`sqrt(11/2(11/2-5)(11/2-1)(11/2-5))`

`=2.49 cm^2`

= Also, area of triangle ADB = 𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝑙𝑒 𝐶𝐷𝐵

∴ Area of the blades of magnetic compass

= 2×(𝑎𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐷𝐵)

= 2 × 2.49

= `4.98 m^2`

#### APPEARS IN

#### RELATED QUESTIONS

Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and (5k – 1, 5k) are collinear.

If the points A(−2, 1), B(a, b) and C(4, −1) are collinear and a − b = 1, find the values of a and b.

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).

Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).

**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)

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:**

Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.

Find the angle subtended at the origin by the line segment whose end points are (0, 100) and (10, 0).

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

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

Show that the points (-3, -3),(3,3) and C (-3 `sqrt(3) , 3 sqrt(3))` are the vertices of an equilateral triangle.

Find the area of ΔABC whose vertices are:

A( 3,8) , B(-4,2) and C( 5, -1)

Find the value(s) of *p* for which the points (3*p* + 1, *p*), (*p* + 2, *p* – 5) and (*p* + 1, –*p*) 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 the area of the following triangle:

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.m^{2}

If Δ = `|(1, x, x^2),(1, y, y^2),(1, z, z^2)|`, Δ_{1} = `|(1, 1, 1),(yz, zx, xy),(x, y, z)|`, then prove that ∆ + ∆_{1} = 0.

In a triangle ABC, if `|(1, 1, 1),(1 + sin"A", 1 + sin"B", 1 + sin"C"),(sin"A" + sin^2"A", sin"B" + sin^2"B", sin"C" + sin^2"C")|` = 0, then prove that ∆ABC is an isoceles triangle.

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 (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}), then `|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|^2 = (3"a"^4)/4`

Show that the points (a + 5, a – 4), (a – 2, a + 3) and (a, a) do not lie on a straight line for any value of a.

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 (a_{1}, b_{1}), (a_{2}, b_{2}) and(a_{1} + a_{2}, b_{1} + b_{2}) are collinear, then ____________.

If the points (2, -3), (k, -1), and (0, 4) are collinear, then find the value of 4k.

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

Points A(3, 1), B(12, –2) and C(0, 2) cannot be the vertices of a triangle.

The area of ∆ABC is 8 cm^{2} in which AB = AC = 4 cm and ∠A = 90º.

The base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. The area of the parallelogram is 30 cm^{2}.

Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per m^{2}.

The area of a trapezium is 475 cm^{2} and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.

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.

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 cm^{2} as shown in the below figure. If altitude QT is 10 cm, then its base PR is ______.

In the given figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is ______.

If area of a triangular piece of cardboard is 90 cm^{2}, then the length of altitude corresponding to 20 cm long base is ______ cm.

Triangles having the same base have equal area.

Area of a triangle PQR right-angled at Q is 60 cm^{2} in the figure. If the smallest side is 8 cm long, find the length of the other two sides.

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 ______.

If (a, b), (c, d) and (e, f) are the vertices of ΔABC and Δ denotes the area of ΔABC, then `|(a, c, e),(b, d, f),(1, 1, 1)|^2` 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 cm^{2} |