IN QUADRILATERAL ABCD SIDE AB PARALLEL SIDE BC SEGMENT AE PERPENDICULAR SEGMENT DC IF LENGTH OF ABIS EQUAL TO,9CM LENGTH OF AE IS EQUAL TO 10 CM AREA OF QUADRILATERAL ABCD IS EQUAL TO 115CM² FIND LENGTH OF DC
Answers
Answer:
The length of DC is 14 cm.
Step-by-step explanation:
Since AB is parallel to DC and AE is perpendicular to DC, then the quadrilateral ABCD is a trapezoid.
The formula in finding the area of trapezoid is
Area = [(b₁ + b₂)h]/2
A = [(DC + AB)(AE)]/2 Substitute.
115 = [(DC + 9)(10)]/2 Substitute the values.
115 = (10DC + 90)/2 Apply cross multiplication.
10DC + 90 = 2(115) Simplify.
10DC + 90 = 230
10DC + 90 + (-90) = 230 + (-90) Applying APE (Addition Property of Equality)
10DC = 140
10DC/10 = 140/10 Applying DPE (Division Property of Equality)
DC = 14 cm
Step-by-step explanation:
Given,
side AB || side DC. l(AB) = 9 cm, l(AE) = 10 cm, A(ABCD) = 115 cm²
∴ ABCD is a trapezium. Area of a trapezium = (1/2) x sum of lengths of parallel sides x height
∴ A(ABCD) = (1/2) x [l(AB) + l(DC) x l(AE)]
∴ 115 = (1/2) x [9 + l(DC)] x 10
∴ (115 x 2)/10 = 9 + l(DC) ∴ 23 = 9 + l(DC)
∴ l(DC) = 23 – 9
∴ l(DC) = 14cm
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