###### Advertisements

###### Advertisements

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

###### Advertisements

#### Solution

We have, the base of a triangle = 4.8 cm

Height of a triangle = 3.6 cm

∴ Area of a triangle = `1/2` × base × height

= `1/2xx4.8xx3.6`

= 8.64 cm^{2}

#### APPEARS IN

#### RELATED QUESTIONS

Find the area of the quadrilateral ABCD whose vertices are respectively A(1, 1), B(7, –3), C(12, 2) and D(7, 21).

Find the area of the triangle whose vertices are: (2, 3), (-1, 0), (2, -4)

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the following figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?

Also calculate the areas of the triangles in these cases. What do you observe?

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

(1, 0), (6, 0), (4, 3)

**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 (1, 2) and (3, 6) using the determinant.

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

**Find the area of the following triangle:**

**Find the missing value:**

Base |
Height |
Area of triangle |

15 cm | ______ | 87 cm^{2} |

ΔABC is right angled at A (see the given figure). AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ΔABC. Also find the length of AD.

Find the area of a triangle whose vertices are

(a, c + a), (a, c) and (−a, c − a)

Prove that the points (2a, 4a), (2a, 6a) and `(2a + sqrt3a, 5a)` are the vertices of an equilateral triangle.

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 ?

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

Prove that the points A(2, 4), b(2, 6) and (2 +`sqrt(3)` ,5) are the vertices of an equilateral triangle

Show that the points (-3, -3),(3,3) and C (-3 `sqrt(3) , 3 sqrt(3))` are the vertices of an equilateral 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 a relation between x and y, if the points A(x, y), B(-5, 7) and C(-4, 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.

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)|` = ______.

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.

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

The value of the determinant `abs((1,"x","x"^3),(1,"y","y"^3),(1,"z","z"^3))` is ____________.

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

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).

The points (1,1), (-2, 7) and (3, -3) are ______.

The area of a triangle with base 4 cm and height 6 cm is 24 cm^{2}.

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}.

Find the area of the trapezium PQRS with height PQ given in figure

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 ______.

In the given figure, ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of ΔACD.

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.