Advertisements
Advertisements
प्रश्न
Find the area of a square inscribed in a circle whose radius is 7 cm (see figure).
[Hint: Four right-angled triangles joined at right angles to form a square]
Advertisements
उत्तर
Given that ABCD is a square
According to the question,
Area of square ABCD = 4 × Area of a right-angled triangle
∴ Area of square ABCD = 4 × Area of ΔAOB
= `4 xx (1/2 xx AO xx BO)` ...`[∵ "Area of a right angled triangle" = 1/2 xx "Base" xx "Height"]`
= 2 × 7 × 7
= 98 cm2 ...[∵ AO = BO = radius of circle = 7 cm, given]
Hence, the area of inscribed square is 98 cm2.
APPEARS IN
संबंधित प्रश्न
The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find its area
The length of the side of the square is given below. Find its area.
12 metre
The table given below contains some measures of the square. Find the unknown values.
| Side | Perimeter | Area |
| ? | ? | 49 sq.feet |
A square park has 40 m as its perimeter. What is the length of its side? Also find its area
The length of the side of a square is given below. Find its area
5 cm
In the following figure, ABCD is a square with AB = 15 cm. Find the area of the square BDFE.
A room is 4.5 m long and 4 m wide. The floor of the room is to be covered with tiles of size 15 cm by 10 cm. Find the cost of covering the floor with tiles at the rate of ₹ 4.50 per tile.
A square tile of length 20 cm has four quarter circles at each corner as shown in the following figure (i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [see figure (ii)]. If the circle touches all four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take π = 3.14)
 |
 |
| (i) | (ii) |
Architects design many types of buildings. They draw plans for houses, such as the plan shown in the following figure:
An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding costs ₹ 500/metre.
- Find how much moulding will be needed for each room.
(i) family room
(ii) living room
(iii) dining room
(iv) bedroom 1
(v) bedroom 2 - The carpet costs ₹ 200/m2. Find the cost of carpeting each room.
- What is the total cost of moulding for all the five rooms.
A square plot has each side measuring 4.5 cm. What is its area?
