Perimeter and Area: questions with answers

Trace A-B-M-D-E-N-G-H-A around the shaded region. MN is an internal line and adds nothing to its perimeter.

Manuring covers the whole surface of the flower bed, so we need its area, not a boundary length. Area of the flower bed = $30 \times 15 = 450$ sq m. Cost of manuring = $450 \times 40 =$ Rs 18000. The park's outer sides are not needed for this cost.

Only the outside boundary is counted. The dashed construction segment is inside the shape and is not part of the perimeter.

For a rectangle, perimeter $=2\times(\text{length}+\text{breadth})$. Here, $2\times(11+10)=2\times21=42$ cm.

A square has four equal sides. Each side is 45 cm, so the perimeter is $4 \times 45 = 180$ cm.

The total boundary length is the perimeter. Add the three side lengths: 8 cm + 12 cm + 14 cm = 34 cm.

The perimeter of a triangle is the sum of the lengths of its three sides. Here the perimeter is 5 cm + 9 cm + 8 cm = 22 cm.

The outside boundary of the design is made of 14 equal small sides. The shared sides inside the design are not part of the perimeter. So 168 = 14 $\times$ side length, and each side is 168 $\div$ 14 = 12 cm.

Count the equal sides on the outside boundary of the zigzag badge. There are 16 boundary sides, and each is 2 cm long. So the perimeter is 16 $\times$ 2 = 32 cm.

Find the whole garden area and subtract the total area of all shaded beds. Whole area = 400 square metres. One bed area = 8 square metres. Total removed area = 24 square metres. Remaining area = 376 square metres.

The two roads cross in the middle, and the part they share is a square of side 4 m. Its area is 4 × 4 = 16 square metres. Riya adds the two full roads and gets 280 + 240 = 520 square metres. That shared square lies inside both roads, so she has counted it twice. The area the roads really cover is 520 − 16 = 504 square metres. So Riya's answer is 16 square metres more.

The full page area is 12 cm x 30 cm = 360 sq cm. The advertisement area is one fourth of this, so it is 90 sq cm. Number of 10 sq cm blocks = 90 / 10 = 9. Cost = 9 x Rs 50 = Rs 450.

Area measures a covered region, so its unit must be a square unit. The side lengths are in cm, so the area is in sq cm, not in cm or sq m.

Each rectangle has area $8 \times 6 = 48$ square units. Triangle ABC is half of it, so its area is 24 square units. Triangle ABE is half of each smaller rectangle, so its area is 6 + 18 = 24 square units. So the two areas are equal, even though the triangles look different.

The part of triangle ABE in the first smaller rectangle has area 12/2 square units. The part in the second smaller rectangle has area 20/2 square units. So the triangle area is (12 + 20)/2 = 16 square units.