Advertisements
Advertisements
प्रश्न
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
To find the area of rhombus, we divide it into two triangles.
As all the sides of a rhombus are equal, we have for a triangle
a = 10, b = 10, c = 16
`s = (a + b + c)/2`
⇒ `s = (10 + 10 + 16)/2 = 36/2 = 18`.
Area (Δ) = `sqrt(s(s - a)(s - b)(s - c))`
⇒ Area (Δ) = `sqrt(18(18 - 10)(18 - 10)(18 - 16))`
⇒ Area (Δ) = `sqrt(18 xx 8 xx 8 xx 2)`
⇒ Area (Δ) = 48 cm2
As the sides of the other triangle are also same, so their areas will also be equal.
Area (Rhombus) = Area (Δ) + Area (Δ)
⇒ Area (Rhombus) = 48 + 48 = 96 cm2
APPEARS IN
संबंधित प्रश्न
There is a slide in the park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.
The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
Sides of a triangle are cm 45 cm, 39 cm and 42 cm, find its area.
Find the areas of the given plot. (All measures are in metres.)
The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.
Using Heron’s formula, find the area of a triangle whose sides are 1.8 m, 8 m, 8.2 m
An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
