Area of Triangle Using Base and Height

The diagonals of a rhombus are $12 \mathrm{cm}$ and $16 \mathrm{cm}$ respectively. Find the length of one side.

If the diagonal of cube is $6\sqrt{3} \mathrm{cm}$, then what is the ratio of the product of total surface area and side of the cube to the volume of the cube?

A right cylindrical vessel is full with water. How many right cones having the same diameter and height as that of the right cylinder will be needed to store that water?

$\mathrm{OABC}$ is a rhombus whose three vertices $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ lie on a circle with centre $\mathrm{O}.$ If the area of the rhombus is $32\sqrt{3} {\mathrm{cm}}^2$, then the radius of the circle is

In Fig.$\mathrm{ABCD}$  is a trapezium with $\mathrm{AB}\parallel \mathrm{DC}$. If $\mathrm{AB}=8 \mathrm{cm}, \mathrm{BC}=\mathrm{CD}=13 \mathrm{cm}$, and $\mathrm{AD}\perp \mathrm{AB}$, then find the area of the trapezium(in square centimetres).

A triangle and a parallelogram have the same base and same area. If the sides of the triangle are $26\mathrm{cm}, 28\mathrm{cm}$ and $30\mathrm{cm}$, and the parallelogram stands on the base $28\mathrm{cm}$, find the height of the parallelogram.

Find the perimeter of an isosceles right-angled triangle having an area of $200$sq cm.

Find the area of a right-angled triangle with hypotenuse $25 \mathrm{cm}$ and base $7 \mathrm{cm}$.

If the difference between the sides (other than hypotenuse) of a right-angled triangle is $3 \mathrm{cm}$ and its area is $54 {\mathrm{cm}}^2$, find its perimeter.

Find the area of a triangle in sq. cm with base $5 \mathrm{cm}$ and whose height is equal to that of a rectangle with base $5 \mathrm{cm}$ and area $20 {\mathrm{cm}}^2$.

Fig. shows an equilateral triangle $ABC$ whose side is $10 \mathrm{cm}$ and a right-angled triangle $BDC$ with side$\text{=8 cm}$. Find the area of the shaded region.

The sides of a triangular field are 320 m, 200 m and 180 m. Using ruler and compasses only, draw the plan of the field using the scale 50 m = 1 cm. Construct the altitude of the triangle on the side measuring 320 m. Measure the altitude and use your result to calculate the area of the actual field in m².

A wire, bent in the form of an equilateral triangle, encloses an area $484\sqrt{3} {\mathrm{cm}}^2$. If the same wire is bent in the form of a circle, find the area and the perimeter of the circle.

From a point in the interior of an equilateral triangle, perpendiculars are drawn on three sides. The lengths of perpendiculars are $14 \mathrm{cm}, 10 \mathrm{cm}$ and $6 \mathrm{cm}$. Find the area of the triangle.

In figure $ABC$ is an isosceles right angled triangle and $DEFG$ is a rectangle. If $AD=AE=3 \mathrm{cm}$ and $DB=EC=4 \mathrm{cm}$. Find the area of the shaded region.

The base of a triangular field is $2.4$ times its height. If the cost of levelling the field at the rate of $₹ 20$ per square meter is $₹ 9600$; find its base and height.

Find the area of a triangle with sides $34 \mathrm{m}, 61.6 \mathrm{m}$ and $34 \mathrm{m}$. Also note the length of the altitude corresponding to the side $61.6 \mathrm{m}$.

The area of an isosceles triangle is $60$ cm² and the length of each one of its equal sides is $13$ cm. Find its base.

The area of an equilateral triangle is $400\sqrt{3}$ sq.units. Its semi-perimeter is $\mathrm{m}$ units. The value of $\mathrm{m}$ is

The base of a right angled triangle is $12 \mathrm{cm}$ and its hypotenuse is $13 \mathrm{cm}$ long. The area of the triangle is $l {\mathrm{cm}}^2$. The value of $\frac{3l}{10}$is