Area Theorems
ICSE · Class 9 · Mathematics
Flashcards for Area Theorems — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedWhy do two parallelograms on the same base and between the same parallels have equal area?
Answer
Step 1: Parallelograms on the same base have the same base length. Step 2: Between the same parallels means they have the same height. Step 3: Area of a parallelogram = base × height. Step 4: Since bo…
Solve: The area of parallelogram AFEC is 140 cm². Find the area of parallelogram BFED if both are on the same base and between the same parallels.
Answer
Step 1: Parallelograms BFED and AFEC are on the same base and between the same parallels. Step 2: Parallelograms on the same base and between the same parallels are equal in area. Step 3: Area of BFED…
Formula for the area of a parallelogram.
Answer
Formula: area of a parallelogram = base × height Here, base = length of the chosen side and height = perpendicular distance between that side and its opposite parallel side. Quick example: If base = 1…
When do you use the rule 'the area of a triangle is half that of a parallelogram on the same base and between the same parallels'?
Answer
Use this rule when a triangle and a parallelogram share the same base and lie between the same parallels. Worked example: If a parallelogram has area 96 cm², then the triangle on the same base and bet…
Solve: Triangle ABC and parallelogram ABDE are on the same base AB and between the same parallels AB and ED. If area of ABDE = 84 cm², find area of triangle ABC.
Answer
Step 1: Triangle ABC is on the same base and between the same parallels as parallelogram ABDE. Step 2: Area of a triangle = 1/2 × area of the parallelogram on the same base and between the same parall…
Why does a triangle have half the area of a parallelogram on the same base and between the same parallels?
Answer
Step 1: A parallelogram can be split by a diagonal into two equal triangles. Step 2: Each triangle has the same base and height as half of the parallelogram. Step 3: So each triangle has half the area…
Formula for the area of a triangle.
Answer
Formula: area of a triangle = 1/2 base × height Here, base = base length and height = perpendicular altitude. Quick example: If base = 10 cm and height = 6 cm, area = 1/2 × 10 × 6 = 30 cm².
Solve: Two triangles are on the same base and between the same parallels. Triangle 1 has area 18 cm². What is the area of Triangle 2?
Answer
Step 1: Triangles on the same base and between the same parallels are equal in area. Step 2: Therefore, Triangle 2 has the same area as Triangle 1. Step 3: Area of Triangle 2 = 18 cm². Answer: 18 cm²…
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