Advertisements
Advertisements
प्रश्न
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
उत्तर
Given that adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm.
Area of parallelogram = Area of ΔADC + area of ΔABC
[∵ Diagonal of a parallelogram divides into two congruent triangles]
= 2 ×[𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐵𝐶]
Now for Area of ΔABC
Let 2s = AB + BC + CA [∵ Perimeter of ΔABC]
`⇒S=1/2(AB+BC+CA)`
`=S=1/2(34+20+42)`
`=1/2=(96)=48cm`
∴Area of ΔABC =`sqrt(s(s-ab))`
`=sqrt(48(48-34)(48-20)(48-42))`
`=sqrt(48(14)(28)(6))=336 cm^2`
∴𝐴𝑟𝑒𝑎 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝐴𝐵𝐶𝐷=2[𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐵𝐶]=2×336=`672 cm^2`
APPEARS IN
संबंधित प्रश्न
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?
A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.
The area of triangle formed by the points (− 5, 0), (0, – 5) and (5, 0) is
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.
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.
Find the area of a parallelogram given in figure. Also find the length of the altitude from vertex A on the side DC.
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
