Area of a Triangle

If the area of the $△XYZ$ is $28 m^2$ and base of the triangle $△PQR$ is $7 cm$ and height is $a cm$. Both the triangles are congruent. Find the value of $a.$

Which two triangles will have equal area.

If the height and base of the$△ABC$ is $10 \mathrm{cm}$ and $8 \mathrm{cm}$, then the area of $△EFG$ is _____ ${\mathrm{cm}}^2$

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.

The area of an equilateral triangle can be found if the altitude is given.

 $\mathrm{OABC}$ 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 $32\sqrt{3} {\mathrm{cm}}^2$, find the radius of the circle.

A pair of bullocks can plough only a portion of a large field $A, B, C, D$, in a day.

The area of the field ploughed by the bullocks is _____ $\mathrm{sq} \mathrm{m}$.

Use the following information to calculate.

$F$ is at a distance of $30 \mathrm{m}$ from $A$ and $B$ the perpendicular distance from to $F$ is $30 \mathrm{m}$.

$E$ is at a distance of $10 \mathrm{m}$ from $D$ and the perpendicular distance from $C$ to E is $40 \mathrm{m}$.

The length of one side of the field $\left(AD\right)$ is $130 \mathrm{m}$.

In the given figure, CD is perpendicular to AC and ∆ABC is an equilateral triangle.

If the area of ∆ACD is 90 sq. m, then the area of ∆ABC is _____$\sqrt{3}$ sq. m.

The area of an equilateral triangle whose side measures 6$ \surd 3$ inches is _____$\sqrt{3}$ sq inch.

The circles shown in the figure are of the same radii $3.2 \mathrm{cm}$.

The area of the triangle formed in the figure is _____$\sqrt{3}$ ${\mathrm{cm}}^2$.

Preeti forms a quadrilateral PQRS by joining two triangular blocks as shown below. The sum of the areas of the two triangles is 192 $ {\text{cm}}^{2}$. She finds that the altitude of Δ$ \text{PSR}$ is 7 cm and PR = 24 cm. The altitude of Δ$ \text{PQR}$ is _____ cm.

The area of given quadrilateral ABCD is

Rita is lost in a maze and walks from points A -> B -> C -> A and then again from A->D-> E-> F -> A covering a total distance of 39 metres. The distance between points A and B is 5 metres. If points ABC form an equilateral triangle and ADEF form a square, the distance between points D and E is _____ metres.

Is the given statement true or false?

If the sides of an equilateral triangle are cut into half to make a smaller triangle, the perimeter of this triangle would be half of the original triangle.

The area of an equilateral triangle is 9√3 sq cm. What is the perimeter of the equilateral triangle?

6 match sticks of length 3 cm each are used to form one equilateral triangle. What is the perimeter of this triangle?

Two equilateral triangles of perimeter 15 cm each are rearranged together to form a hexagon. The perimeter of the hexagon is

An equilateral triangle has its sides measuring 10 cm. Is there any data missing to calculate the perimeter of the triangle?