Heron's Formula Quiz

A parallelogram has 60 m and 25 m and a diagonal 6500 cm long. Find the area of the parallelogram.

1. 10000 m2
2. 1500 m2
3. 750 m2
4. 150000 m2

Answer: (b) 1500 m2

If (s - a) = 7 cm, (s - b) = 8 cm, (s - c) = 3 cm, where a, b and c are the sides of triangle. What is the value of a, b and c?

1. a = 11 cm, b = 10 cm, c = 15 cm
2. a = 10 cm, b = 14 cm, c = 11 cm
3. a = 5 cm, b = 20 cm, c = 15 cm
4. a = 12 cm, b = 9 cm, c = 15 cm

Answer: (a) a = 11 cm, b = 10 cm, c = 15 cm

Find the cost of leveling the ground in the form of an equilateral triangle whose side is 12 m at $5 per m2.

1. $100.56
2. $319.23
3. $311.4
4. $187.65

Answer: (c) $311.4

The sides of a triangle are x, x + 1, 2x - 1 and its area is x √10 m2. Find the value of x.

1. 10 m
2. 2 m
3. 8 m
4. 6 m

Answer: (d) 6 m

A triangle has two sides of lengths 26 cm and 28 cm. The perimeter of the triangle is 84 cm. If the triangle is placed on a horizontal plane with the base being the longest side. If a rectangle is inscribed within this triangle such that its width equals half the base and its height is equal to the height of the triangle, find the area of the rectangle.

1. 316 cm2
2. 336 cm2
3. 415 cm2
4. 130 cm2

Answer: (b) 336 cm2

Find the area of the shaded region in the given figure.

1. 384 cm2
2. 380 cm2
3. 157 cm2
4. 623 cm2

Answer: (a) 384 cm2

The perimeter of a triangle is x cm, and its sides are represented by p cm, q cm, and r cm. The sides p, q, and r are in the ratio 3 : 4 : 5. The perimeter is increased by 20% to form a new triangle with sides p', q', and r'. Calculate the difference in area between them.

1. 0.44x2
2. 0.44x2/15
3. 0.11x2/6
4. 0.53x2/2

Answer: (c) 0.11x2/6

Read the passage and answer the following question. Triangles are used in bridges because they evenly distribute weight without changing their proportions. When force is applied to a shape like a rectangle, it would flatten out. Before triangles were used in bridges, they were weak and could not be very big. To solve that problem, engineers would put a post in the middle of a square and make it more sturdy. Isosceles triangles were used to construct a bridge in which the base (unequal side) of an isosceles triangle is 4 m and its perimeter is 20 m. What is the length of equal sides?

1. 10 m
2. 2 m
3. 6 m
4. 8 m

Answer: (d) 8 m

Read the passage and answer the following question. Triangles are used in bridges because they evenly distribute weight without changing their proportions. When force is applied to a shape like a rectangle, it would flatten out. Before triangles were used in bridges, they were weak and could not be very big. To solve that problem, engineers would put a post in the middle of a square and make it more sturdy. Isosceles triangles were used to construct a bridge in which the base (unequal side) of an isosceles triangle is 4 m and its perimeter is 20 m. If the new area is √15 times larger than the previous area, find the height.

1. 15 m
2. 30 m
3. 13 m
4. 20 m

Answer: (b) 30 m

Read the passage and answer the following question. In my colony, a park is situated in front of my house. This park is built in the shape of a triangle (ABC) with the following sides 120 m, 80 m and 50 m. Now-a-days, some animals enter parks and destroy and eat plants. So, our ward member of the area has decided to put railing around the park for protecting plants and grass. A ward member ordered a gardener to place a railing all around this park and maintain grass inside the park. He also sanctioned an amount to improve the park in a proper way for public of that colony. Costing is decided $ 10 per meter for railing around the park. Determine the area of the triangular park.

1. 371 m2
2. 45√15 m2
3. 125√15 m2
4. 375√15 m2

Answer: (d) 375√15 m2