MEDIUM
Earn 100

Show that the ratio of the areas of two triangles of the same base is equal to the ratio of their heights.

Important Questions on Geometry

EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The area of a right angled triangle having base 24 cm and hypotenuse 25 cm is_____.
MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

In △ABC, AD is the median and G is a point on AD such that AG:GD=2:1. Then area (△BDG):area (△ABC) is equal to:

EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Triangle PDC is drawn inside the square ABCD of side 24 cm where P lies on AB. What is the area of the triangle?
MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
In a triangle, angles are in the ratio of 1:1:2 and the length of its longest side is 62 cm, then what is the Area (in cm2) of the triangle?
MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The length of each equal side of an isosceles triangle is 10 cm and the included angle between those two sides is 45°.Find the area of the triangle.
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The sides of an isosceles triangle are 10 cm, 10 cm and 12 cm. What is the area of the triangle?
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The length of each equal side of an isosceles triangle is 15 cm and the included angle between those two sides is 90°, Find the area of the triangle.
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

The hypotenuse of a right-angled triangle is 39 cm and the difference of other two sides is 21 cm. Then, the area of the triangle is:

MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

The three sides of a triangle are 15 cm, 36 cm, and 39 cm long. A small triangle is formed by joining the mid points of the three sides of this triangle. The area of small triangle will be_____ cm2  

HARD
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
What will be the area of triangle whose vertices are (1, 2), (-4, -3) and (4, 1)?
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
If the height of an equilateral triangle is 202 cm, then what is its area (in cm2)?
MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Consider four triangles having sides 5,12,9, 5,12,11,5,12,13 and 5,12,15 . Among these the triangle having maximum area has sides
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The base and hypotenuse of a right-angled triangle are 9 cm and 41 cm respectively. What is the area of the reiangle?
HARD
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
In a quadrilateral ABCD, it is given that AB=AD=13, BC=CD=20, BD=24. If r is the radius of the circle inscribable in the quadrilateral, then what is the integer closest to r ?
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The side of an equilateral triangle is 4 cm. Wat is its area?
MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
If a, b, c are the sides of a ∆ABC and exradii r1, r2, r3 are respectively 12, 6, 4 then a+2b+3c= 
MEDIUM
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
What is the area of the triangle having sides 35 cm, 84 cm and 91 cm?
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
What is the area (in cm2) of an equilateral triangle whose side is 12 cm?
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
A triangular corner is cut from a rectangular piece of paper and the resulting pentagon has sides 5,6,8,9,12 in some order. The ratio of the area of the pentagon to the area of the rectangle is-
EASY
Mathematics>Geometry>Geometry>Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
If the sides of triangle are 4,5 and 6 cm . Then the area (in sq cm) of triangle is