Advertisements
Advertisements
Question
A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.
Advertisements
Solution
Perimeter of the rhombus = 160 m
4 × side = 160
Side of a rhombus = `160/4`
= 40 m
In ΔABC, a = 40 m, b = 40 m, c = 48 m
s = `("a" + "b" + "c")/2`
= `(40 + 40 + 48)/2 "cm"`
= `128/2`
= 64 m
s – a = 64 – 40 = 24 m
s – b = 64 – 40 = 24 m
s – c = 64 – 48 = 16m
Area of the ΔABC = `sqrt(64 xx 24 xx 24 xx 16)`
= 8 × 24 × 4
= 768 sq.m
Since ABCD is a rhombus Area of two triangles are equal.
Area of the rhombus ABCD = (768 + 768) sq.m
= 1536 sq.m
∴ Area of the land = 1536 sq.m
APPEARS IN
RELATED QUESTIONS
A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
Area of PQRS = Area of PQR + Area of ΔPQS = (6+9.166)𝑐𝑚2=15.166𝑐𝑚2
The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 meters respectively, and the angle contained by the first two sides is a right angle. Find its are
Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.
The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is
The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?
In the given figure, the ratio AD to DC is 3 to 2. If the area of Δ ABC is 40 cm2, what is the area of Δ BDC?
If the length of a median of an equilateral triangle is x cm, then its area is
