Online Test — Areas of Parallelograms and Triangles
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
If two geometric figures are completely congruent, what can we conclude about their surface areas?
They are unequal
They are equal
One is double the other
No relation exists
Explanation: By the Congruence Area Property, identical shapes always enclose identical areas.
Question 2 of 10
medium
A parallelogram has a base length of 12 cm and a height of 7 cm. What is its total surface area?
42 sq cm
84 sq cm
24 sq cm
19 sq cm
Explanation: Area of a parallelogram = base × height = 12 × 7 = 84 sq cm.
Question 3 of 10
medium
A triangle has a base of 10 cm and an area of 40 sq cm. Calculate its corresponding perpendicular height.
4 cm
8 cm
12 cm
16 cm
Explanation: Area = 0.5×b×h -> 40 = 0.5×10×h -> 40 = 5×h -> h = 8 cm.
Question 4 of 10
medium
A triangle and a parallelogram stand on the same base and between the same parallels. If the triangle's area is 25 sq cm, find the parallelogram's area.
12.5 sq cm
25 sq cm
50 sq cm
100 sq cm
Explanation: Area of the parallelogram is double the triangle's area: 2 × 25 = 50 sq cm.
Question 5 of 10
medium
Two parallelograms stand on the same base and between the same parallel lines. If the area of the first is 60 sq cm, the area of the second is:
30 sq cm
60 sq cm
120 sq cm
180 sq cm
Explanation: Parallelograms on the same base and parallels have completely equal areas.
Question 6 of 10
medium
A median of a triangle divides it cleanly into two smaller sub-triangles. What is the area relationship between these two parts?
First is double the second
They have equal areas
They have unequal areas
One is triple the other
Explanation: A median splits a triangle into two triangles with equal bases and the same height.
Question 7 of 10
medium
If the base of a triangle is doubled while its vertical height stays exactly the same, what happens to its total area?
It stays the same
It is halved
It is doubled
It is quadrupled
Explanation: Area is directly proportional to base. Doubling the base doubles the area.
Question 8 of 10
medium
A rectangle and a parallelogram share the same base and have equal areas. What can you say about their perimeters?
Rectangle has a larger perimeter
They have equal perimeters
Parallelogram has a larger perimeter
Cannot be determined
Explanation: The slanted sides of the parallelogram are longer than the vertical sides of the rectangle.
Question 9 of 10
medium
Can two non-congruent shapes have the exact same surface area value?
No, never
Yes, always
Yes, it is possible
Only if they are circles
Explanation: Shapes can have different designs but enclose the same total space (e.g., 6×4 rect vs 8×3 rect).
Question 10 of 10
medium
If a triangle has sides measuring 6 cm, 8 cm, and 10 cm, what is its calculated area? (Hint: it is a right-angled triangle).
48 sq cm
24 sq cm
14 sq cm
40 sq cm
Explanation: Base and height are 6 and 8 (10 is hypotenuse). Area = 0.5 × 6 × 8 = 24 sq cm.