The area of triangles can be found by using the following formula:
Area = Base × height / 2
The red line represents the length of the base (call it b if you want) and the blue line represents the length of the height.
To get the area, just multiply the value of the base by the value of the height and divide the result by 2.
Example:
Find the area for the following figure:
The area is 18 square inches or 18 inches2.
Condition of collinearity of three points
Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line.
There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.
In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is,
either AB + BC = AC or AC +CB = AB or BA + AC = BC.
In other words,
There points A, B and C are collinear if:
AB + BC = AC i.e., Or,
(ii) AB + AC = BC i.e. ,
Or, AC + BC = AB i.e.,
Measure of angles
In the sexagesimal
In Sexagesimal System, an angle is measured in degrees, minutes and seconds.
A complete rotation describes 360°. In this system, a right angle is divided into 90 equal parts and each such part is called a Degree (1°); a degree is divided into 60 equal parts and each such part is called a Sexagesimal Minute (1’) and a minute is further sub-divided into 60 equal parts, each of which is called a Sexagesimal Second (1’’). In short,
1 right angle = 90 degrees (or 90°)
1 degree (or 1°) = 60 minutes ( or 60’)
1 minute ( or 1’ ) = = 60 seconds ( or 60’’)
In Centesimal System
In Centesimal System, an angle is measured in grades, minutes and seconds. In this system, a right angle is divided into 100.
equal parts and each such part is called a Grade (1g); again, a grade is divided into 100 equal parts and each such part is called a Centesimal Minute (1‵) ; and a minute is further sub-divided into 100 equal parts, each of which is called a Centesimal Second (1‶). In short,
1 right angle = 100 grades (or, 100g)
1 grade ( or 1g) = = 100 minutes (or, 100‵)
and 1 minute (or 1‵) = = 100 seconds ( or, 100‶).
Circular System
In this System, an angle is measured in radians. In higher mathematics angles are usually measured in circular system. In this system a radian is considered as the unit for the measurement of angles.
Radian: A radian is an angle subtended at the center of a circle by an arc whose length is equal to the radius.
In any circle, the angle subtended at its centre by an arc of the circle whose length is equal to the radius of the circle is called a radian. Let OX = r be the radius of a circle having center at O
Now, take an arc XY of the circle such that arc XY = r and join OY. By definition, ∠XOY = one radian. One radian is written as 1c, 2 radians as 2c and in general, k radians as kc.
Circular (radian) measure of an angle:
The circular measure of an angle is the number of radians it contains. Thus the circular (radian) measure of a right angle is π/2.
,
The area of a triangle is the amount of space enclosed by the triangle’s three sides. It can be calculated using the following formula:
$$A = \frac{1}{2}bh$$
where $b$ is the base of the triangle and $h$ is the height of the triangle.
The base of a triangle is the side that is opposite the right angle in a right triangle, or any side of a triangle that is not the height. The height of a triangle is the perpendicular distance from the base to the opposite vertex.
Heron’s formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is given by the following formula:
$$A = \sqrt{s(s-a)(s-b)(s-c)}$$
where $s$ is the semiperimeter of the triangle, which is given by the following formula:
$$s = \frac{a+b+c}{2}$$
The area of a right triangle can be calculated using the following formula:
$$A = \frac{1}{2}bh$$
where $b$ is the base of the triangle and $h$ is the height of the triangle. The height of a right triangle is the perpendicular distance from the hypotenuse to the opposite vertex.
The area of an equilateral triangle can be calculated using the following formula:
$$A = \frac{\sqrt{3}}{4}s^2$$
where $s$ is the side length of the triangle.
The area of an isosceles triangle can be calculated using the following formula:
$$A = \frac{1}{2}bh$$
where $b$ is the base of the triangle and $h$ is the height of the triangle. The height of an isosceles triangle is the perpendicular distance from the base to the vertex opposite the base.
The area of a scalene triangle can be calculated using the following formula:
$$A = \frac{1}{2}bh$$
where $b$ is the base of the triangle and $h$ is the height of the triangle. The height of a scalene triangle is the perpendicular distance from the base to the vertex opposite the base.
The area of a triangle is a useful quantity to know for many different applications. For example, it can be used to calculate the amount of material needed to build a roof, the amount of paint needed to cover a wall, or the amount of land that is enclosed by a fence.
What is the Pythagorean Theorem?
The Pythagorean Theorem is a mathematical formula that relates the lengths of the sides of a right triangle. It states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides.
What is the formula for the Pythagorean Theorem?
The formula for the Pythagorean Theorem is $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the other two sides of the triangle and $c$ is the length of the hypotenuse.
What is the area of a triangle?
The area of a triangle is equal to one half the product of the base and height of the triangle.
What is the formula for the area of a triangle?
The formula for the area of a triangle is $A = \frac{1}{2}bh$, where $b$ is the base of the triangle and $h$ is the height of the triangle.
What is the perimeter of a triangle?
The perimeter of a triangle is the total length of all three sides of the triangle.
What is the formula for the perimeter of a triangle?
The formula for the perimeter of a triangle is $P = a + b + c$, where $a$, $b$, and $c$ are the lengths of the three sides of the triangle.
What is the centroid of a triangle?
The centroid of a triangle is the point of intersection of the medians of the triangle.
The median of a triangle is a line segment that joins a vertex of the triangle to the midpoint of the opposite side.
What is the orthocenter of a triangle?
The orthocenter of a triangle is the point of intersection of the altitudes of the triangle.
What is the altitude of a triangle?
The altitude of a triangle is a line segment that is perpendicular to the base of the triangle and passes through a vertex of the triangle.
What is the circumcenter of a triangle?
The circumcenter of a triangle is the point of intersection of the circumcircles of the triangle.
What is the circumcircle of a triangle?
The circumcircle of a triangle is a circle that passes through all three vertices of the triangle.
What is the incenter of a triangle?
The incenter of a triangle is the point of intersection of the incircles of the triangle.
What is the incircle of a triangle?
The incircle of a triangle is a circle that is inscribed in the triangle, meaning that it touches all three sides of the triangle.
What is the Euler line of a triangle?
The Euler line of a triangle is a line that passes through the centroid, orthocenter, and circumcenter of the triangle.
What is the nine-point center of a triangle?
The nine-point center of a triangle is the point of intersection of the nine-point lines of the triangle.
What is the nine-point line of a triangle?
The nine-point line of a triangle is a line that passes through the midpoints of the sides of the triangle and the feet of the altitudes of the triangle.
What is the circumradius of a triangle?
The circumradius of a triangle is the radius of the circumcircle of the triangle.
What is the inradius of a triangle?
The inradius of a triangle is the radius of the incircle of the triangle.
What is the area of a circle?
The area of a circle is equal to pi times the square of the radius.
What is the formula for the area of a circle?
The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius of the circle.
What is the circumference of a circle?
The circumference of a circle is equal to two times pi times the radius.
What is the formula for the circumference of a circle?
The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the circle.
What is the diameter of a circle?
The diameter of a circle is a line segment that passes through the center of the circle and has endpoints on the circle.
What is the formula for the diameter of a circle?
The formula for the diameter of a circle is $d
The area of a triangle is equal to one half the product of its base and height. True or False?
The area of a triangle is equal to the square of its side divided by four. True or False?
The area of a triangle is equal to the product of its base and height divided by two. True or False?
The area of a triangle is equal to the square of its side divided by six. True or False?
The area of a triangle is equal to the product of its base and height divided by three. True or False?
The correct answer is: 3.
The area of a triangle is equal to the product of its base and height divided by two. This can be written as $A = \frac{1}{2}bh$, where $b$ is the base of the triangle and $h$ is the height of the triangle.
The other Options are all incorrect. Option 1 is incorrect because the area of a triangle is not equal to one half the product of its base and height. Option 2 is incorrect because the area of a triangle is not equal to the square of its side divided by four. Option 4 is incorrect because the area of a triangle is not equal to the square of its side divided by six. Option 5 is incorrect because the area of a triangle is not equal to the product of its base and height divided by three.
