Area of Parallelograms and Triangles Worksheet 1 with Answers
1. In the following figure p || q,
area of ΔABC is 36 sq. units, then what will be the area of ΔBAD?
2. In the given figure, ABCD is a rectangle and X
is any point on CD such that the area of ΔAXB = 16 cm2. Find the
area of the rectangle ABCD.
3. In the given figure, BC || XY. Show that area
(ΔOBX) = area (ΔOCY).
4. In the given figure, find the height of ΔPOS.
5.
State true or false.
a.
Parallelograms with equal bases and between the same parallel lines are equal
in area.
b.
A diagonal of a parallelogram divides it into two congruent triangles having
different area.
c. If the area of a triangle is 25.5 cm2, then 51 cm2
is the area of a parallelogram when triangle and parallelogram are on the same
base and between the same parallel lines.
6. In the given figure two ||gms PQRS and PQZY
are shown. If the area of ||gm PQRS is 38.4 cm2 and PQ = 6 cm, then
find the height of ||gm PQZY.
7. In the given figure, AD and BE are medians of ΔABC and ΔABD respectively. Show that area (ΔBEC) = area (ΔABD).
8. In the given figure, ABCD is a parallelogram
and AD || FE || BC. Prove that area (ΔAEB) = area (ΔDFC).
9. In the given figure, ABCD and ABEF are two parallelograms on the same base AB. Show that area (ΔADB) = area (ΔEBF).
Area of
Parallelograms and Triangles Worksheet 2 with Answers
1. In the given figure ABCD is a square of side 13 cm and ABEF is a parallelogram. Find
a. the area of || gm ABEF
b.
the area of ΔXEF
2. Given two parallelograms ABCD and
EFCD. Show that area (ΔMAC) = 1/2 area (||gm ABCD)
3. PQRS is a parallelogram where PN ⊥ RS and RT ⊥ PS. If QR = 10 cm, RT = 9 cm and PN = 4 cm, find RS.
4. ABDC is a parallelogram. E and F are the
midpoints of sides AC and BD respectively. Show that area (|| gm ABFE) = area
(|| gm CDFE).
5. In the given figure, O is a point in the interior of a parallelogram ABCD. Show that area (ΔAOD) + area (Δ OBC) = area (ΔAOB) + area (ΔCOD)
6. Given
ABCD is a quadrilateral and area (ΔAOD) = area (BOC). Show that the
quadrilateral is a parallelogram.
7.
In the given figure, E is any point on the
median AD of ΔABC. Show that
a.
area (Δ EDB) = area (ΔEDC)
b. area (ΔABE) =
area (ΔACE)
8. ABCD is parallelogram. Given, AM⊥
BC, CN⊥AD such that CM = AN. Prove that area (Δ ABM)
= area (Δ CDN).
ANSWERS
Worksheet 1
1. 36 sq. units 2. 32 cm2
3. Do it yourself
4. 3 cm
5. a. True b. False
c. True
6. 6.4 cm
7. Do it yourself
8. Do it yourself
9. Do it yourself
Worksheet 2
1. a. 169 cm2 b. 84.5 cm2
2. Do it yourself
3. 22.5 cm
4. Do it yourself
5. Do it yourself
6. Do it yourself
7. Do it yourself
8. Do it yourself
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